Dr.  Lalit  Kumar  (Ph. D.   University of Delhi)

Professor 

Department of Mathematics 

University of Delhi

Delhi -110 007.

Phone Office: +91-011-27666658

Email:  lalit@maths.du.ac.in,    lkumarvashisht@gmail.com

 My Research Interests

Frames for Banach Spaces;  Hilbert Frames; Wavelet Analysis;

 Fourier analysis;  Functional Analysis.

ORCID:  https://orcid.org/0000-0002-8634-6920 

Research Publications 

1.  Hamiltonians defined by Hilbert-Schmidt  Riesz bases and frames, submitted.   (with Jyoti). 

2.  On convex sums of Hilbert-Schmidt frames,  submitted. (with Jyoti and P. E. T. Jorgensen).

3.  On spectral properties of the Hilbert-Schmidt frame operator, submitted. (with Jyoti). 

4.  On perturbation of Hilbert-Schmidt frames,  Bulletin  of  the  Malaysian  Mathematical Sciences Society,  49 (3)  (2026), Art. No.  106, 18pp .  (with Jyoti) . MR5065884,  Zbl xxxx.xxxxx . 

5.  Discrete frames of non-uniform shifts in frequency domain,  Mathematical  Methods in the Applied Sciences,   (2026), 1-20.  (with H. K. Malhotra and M. Chhillar). 

6.  Sums of frames from the Weyl-Heisenberg group and applications to frame algorithm,  Advances  in Pure and  Applied Mathematics,  17 (2), 1-19  (2026).  (with D. Jindal and Jyoti).  MR5049884,  Zbl 08195434.

7.  Frames for source recovery from non-uniform dynamical  samples,  International Journal of  Wavelets,  Multiresolution  and  Information  Process,  24  (2)  (2026),   Art. No. , 2550045,  38 pp.  (with  Ruchi).   MR5043289,  Zbl 08187389.

8.  Operators for matrix-valued Riesz bases over LCA groups,  Results  in Mathematics,  80  (8)  (2025),  Art. No. 224, 19pp . (with Jyoti).  MR4984456,  Zbl 08122719.

9.  Hilbert-Schmidt frames and Riesz bases with respect to tensor product of Hilbert spaces,  Analysis  Mathematica,  51 (3) ,  843-865 (2025).  (with Jyoti).  MR4977111,  Zbl 08132892.

10.  A note on matrix-valued orthonormal bases over LCA groups,  Infinite  Dimensional  Analysis, Quantum Probability and Related Topics,  28 (3)  (2025),  Art. No.  2450006,  12 pp.  (with Jyoti).  MR4972337,  Zbl 08109223.

11.  Perturbation of frames from the Weyl-Heisenberg group and the extended affine group,  Complex Analysis and Operator Theory,  19  (3) (2025),  Art. No.  54,  33 pp.  (with D. Jindal and Palle Jorgensen).  MR4878978,  Zbl  1565.42022.

12.  On matrix-valued Riesz bases over LCA groups,  International Journal of  Wavelets,  Multiresolution  and  Information  Process,  22  (5)  (2024),   Art. No. 2450019, 1--16.  (with Jyoti). MR4787644,  Zbl  1545.42031.

13.  Nonstationary matrix-valued multiresolution analysis from the extended affine group,  Analysis  Mathematica,  50 (1),  189--213 (2024).  (with D. Jindal).  MR4740661,    Zbl 1563.42081.

14.  On matrix-valued Gabor frames over locally compact abelian groups,  Infinite  Dimensional  Analysis, Quantum Probability and Related Topics,  26 (4)  (2023),  Art No. 2350023,  20 pp.    (with U.K.Sinha and P.K. Das). MR4683214,  Zbl 1530.42055.

15.  On Hilbert-Schmidt frames for operators and Riesz bases,  Journal  of  Mathematical Physics,  Analysis,  Geometry,  19 (4),  799--821  (2023).   (with Jyoti).  MR4680864,   Zbl 1542.42035.

16.   Nonstationary frames of translates  and frames for the Weyl-Heisenberg group and the extended affine group,  Journal  of  Physics  A:   Mathematical and Theoretical,   56 (34) (2023),  Art. No. 345204, 20pp.  (with D. Jindal). MR4634063,  Zbl 1525.42031.

17.   Matrix-valued  Gabor frames over LCA Groups for  Operators,  Filomat,  37 (28) (2023), 9543-9559.  (with Jyoti and U.K. Sinha). MR4644620.

18.  Matrix-valued nonstationary frames associated with the Weyl-Heisenberg group and extended affine group,  International Journal of  Wavelets,  Multiresolution  and  Information  Process,  21  (6)  (2023),  25 pp.   (with D. Jindal and Jyoti).  MR4641836,  Zbl  1528.42041.

19.  On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups,    Khayyam Journal  of  Mathematics,  9 (1)   (2023),  89-101.   (with U. K. Sinha).   MR4536343,  Zbl 1513.42141.

20.  Frames with several generators  associated with Weyl-Heisenberg group and extended affine group, Bulletin  of  the  Malaysian  Mathematical Sciences Society,  45 (5)  (2022),  2413-2430.  (with D. Jindal). MR4489569,  Zbl 1505.42034.

21.  Discrete vector-valued nonuniform Gabor frames,  Bulletin  des  Sciences Mathematiques,  178   (2022),  Paper  No.  103145,  34 pp.  (with H. K. Malhotra).  MR4428742,    Zbl1491.42047.

22.  Duality for  matrix-valued  wave packet frames in L^2(R^d, C^(s x r)),   International Journal of  Wavelets,  Multiresolution  and  Information  Process,  20 (4)   (2022),  Paper No. 2250007,  20 pp.  (with Jyoti).  MR4458453,   Zbl1504.42088.

23.  On the paper ``Characterizations of weaving for g-frames by induced sequences'' ,  arXiv.211.05612v2. (wth Deepshikha and G. Verma).

24.  On vector-valued nonuniform multiresolution analysis,  Applicable Analysis,  101 (17)  (2022),  6013-6027.  (with H.K. Malhotra).  MR4486470,   Zbl 1506.42041.

25.  Construction of P^th -stage nonuniform  discrete wavelet  frames,   Results  in Mathematics,  76 (3)   (2021),  Art.  No.  117,   30 pp.   (with H.K. Malhotra).    MR4261749,   Zbl1467.42048.

26.  Unitary extension principle for non-uniform wavelet frames in L^2(R),  Journal of Mathematical Physics, Analysis,  Geometry,    17 (1)   (2021),  79--94.  (with H.K. Malhotra). MR4263894,    Zbl  1488.42161.

27.  On Matrix-valued  wave packet frames in L^2(R^d, C^(s x r)),   Analysis and Mathematical Physics,   10  (4)  (2020),   Art. No.  66,   24 pp.  (with Jyoti)   MR4169373,   Zbl1455.42029.

28.  On scaling functions of non-uniform multiresolution analysis in L^2(R),  International Journal of Wavelets,  Multiresolution  and  Information  Process,  18 (2)  (2020),  14 pp.  (with H.K. Malhotra).  MR4079091,   Zbl 1442.42079.

29.  Operators related to the reconstruction property in Banach spaces,  Results  in Mathematics,  74 (3)   (2019),  Art.  No. 125,   17 pp.    (with Jyoti and G. Verma) MR3958787,   Zbl1419.42027.

30.  On excess of retro Banach frames,   Izvestiya  Natsional'naya   Akademiya  Nauk  Armenii  Matematika   (reprinted in the Journal of Contemporary Mathematical Analysis),  54 (3)  (2019),  129-132.    (with G. Verma).   MR3979969.  Zbl 1437.42051.

31.  Vector-valued (Super) weaving frames,  Journal of Geometry and  Physics,  134  (2018),  48--57.   (with Deepshikha).  MR3886925 ,  Zbl 1403.42036.

32.  K-Matrix-valued  wave packet frames in L^2(R^d, C^(s x r)),  Mathematical Physics,  Analysis and Geometry,  21 (3)  (2018),  Art. No.  21, 19 pp.  (With Jyoti).  MR3835627,     Zbl1396.41020.

33.  Weaving K-frames in Hilbert spaces,   Results  in Mathematics,  73 (2) (2018),  Art. No.  81,   20 pp.   (with Deepshikha).   MR3805557,  Zbl 1407.42022

34.  On weaving frames,  Houston Journal of  Mathematics,  44 (3) (2018),  887--915.  (with Deepshikha).    MR3879982,  Zbl 1412.42075.

35.  On generalized weaving frames in Hilbert spaces,  Rocky Mountain Journal of Mathematics,  48 (2) (2018),  661--685.   (with S. Garg, Deepshikha and P.K. Das).  MR3810464,   Zbl1392.42030.

36.  Sums of matrix-valued wave packet frames in  L^2(R^d, C^(s x r)),  Glasnik   Matematicki ,   53 (1) (2018) , 153--177.  (with Jyoti, Deepshikha and G. Verma)   MR3814235,   Zbl1464.42026.

37.  On WH-packets of matrix-valued wave packet frames in L^2(R^d, C^(s x r)),  International Journal of Wavelets Multiresolution  and  Information  Process, 16 (3) (2018) 1850022 (22 pages) (with Jyoti).  MR3805708,  Zbl 1396.42008.

38.  Traces of Hadamard and Kronecker products of matrices,  Mathematics for  Applications  (Brno),  6 (2017),  143--150 (with P. K. Das)  MR3742414, Zbl 1386.15042.

39.  Generalized weaving frames for operators in Hilbert spaces,  Results  in Mathematics,  72 (3) (2017), 1369--1391 (with Deepshikha and   Geetika Verma). MR3721620,    Zbl1385.42028 .

40.  Frames in topological algebras,  Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math.Phys.,  79 (3) (2017), 163-170.  (with Saakshi Garg)  MR3703289.

41.  Weaving K-fusion frames in Hilbert spaces, Ganita, 67 (1) (2017),  41--52.  (with Saakshi Garg)  MR3785319 .

42.  Extension of Bessel sequences to dual frames in Hilbert spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys.,  79 (2) (2017),  71--82. (with Deepshikha). MR3678067

43.  Necessary and sufficient conditions for discrete wavelet frames in  C^N,  Journal of Geometry and  Physics,  117 (2017), 134--143. (with Deepshikha) MR3645837,     Zbl1364.42035.

44.  On Continuous weaving frames,   Advances  in  Pure and  Applied  Mathematics,   8 (1) (2017),  15--31. (with Deepshikha) MR3592583,    Zbl 1365.42028.  

45.  Weaving properties of generalized continuous frames generated by an iterated function system, Journal of  Geometry and  Physics., 110 (2016),  282--295. (with Deepshikha) MR3566116,    Zbl 1417.42038.

46.  On perturbation of frames in locally convex spaces,  Jordan Journal of Mathematics and  Statistics,  9 (4) (2016),  271--281  (with S. Garg and G. Khattar).  MR3603193,  Zbl1362.42068.

47.  A note on discrete frames of translates in C^N,   TWMS Journal of  Applied  and Engineering  Mathematics,   6 (1) (2016),  143--149.  (with Deepshikha)  MR3594863,  Zbl1371.42038.

48.  Extension of Weyl-Heisenberg wave packet Bessel sequences to dual frames in L^2(R),  Journal of Classical  Analysis,   8 (2) (2016), 131--145. (with Deepshikha).   MR3535232

49.  Error locating codes by using blockwise-tensor product of blockwise detecting / correcting codes, Khayyam Journal of Mathematics,  2 (1) (2016), 6--17. (with P. K. Das)  MR3577213 ,    Zbl 138094144.

50.  On exact frames in topological algebras, Palestine  Journal of  Mathematics,  5 (1) (2016), 131--134. (with Saakshi Garg )  MR3413765,   Zbl 137742032.

51.  On perturbation of binary linear codes,  Mathematics for Applications  (Brno),  4 (2015),  91--99  (with P. K. Das)  MR3437508,   Zbl 1370.94573 .

52.  Banach frames generated by compact operators associated with a boundary value problem,  TWMS  Journal  of Pure  and Applied  Mathematics,  6 (2) (2015),  254--258.  MR3689356,   Zbl 1348.42041.

53.  Some types of convergence related to the reconstruction property in Banach spaces,   Banach Journal of Mathematical  Analysis,   9 (2) (2015),  253--275. (with G. Khattar) MR3296117,   Zbl 1311.42082 . 

54.   Irregular Weyl-Heisenberg  wave packet frames in  L^2(R),   Bulletin des  Sciences Mathematiques,  139 (1)  (2015),   61--74. (with A.K. Sah )  MR3312288,   Zbl 1307.42031.

55.  The reconstruction property in Banach spaces generated by matrices,   Advances  in  Pure and  Applied  Mathematics,  5 (3) (2014), 151-160.(with G. Khattar)    MR3259018,  Zbl1297.42044. 

56.  Frames of eigenfunctions associated with a boundary value problem,  International  Journal of  Analysis,  Vol. 2014 Article Id. 590324. 6 pages, 2014. doi: 10.1155/2014/590324 (with Shalu Sharma)  MR3219410,  Zbl 1390.46026.

57.  Reconstruction property and frames in Banach spaces, Palestine  Journal of  Mathematics,  3(1) (2014), 11--26.  (with S.K.Kaushik and G.Khattar)   MR3109934,   Zbl 1389.42064

58.  On I-reconstruction property,  Advances in  Pure Mathematics,  3 (3) (2013), 324 --330.  ( with G. Khattar)  doi:10.4236/apm.2013.33046..

59.  Some results concerning frames associated with measureable spaces,   TWMS Journal  of  Pure  and Applied  Mathematics,  4 (1) (2013), 52-60. (with S.K. Kaushik and S.K.Sharma)  MR3097680,  Zbl 1312.42034.

60.  On Φ-Schauder frames,  TWMS Journal of  Applied  and Engineering  Mathematics,   2 (1) (2012), 116-120.  MR3068866,   Zbl  1274.42080.

61.  On retro Banach frames of type P,   Azerbaijan .Journal of  Mathematics,   2 (1) (2012), 82-89. MR2967281,  Zbl 1278.42041. 

62.  On stability of Banach frames,  Bulletin of the  Korean Mathematical  Society,   44 (2007), no. 1, 73-81. (with P.K.Jain and S.K. Kaushik)  MR2297696,   Zbl1190.42013.

63.  On Banach frames,  Indian Journal of  Pure  and Applied  Mathematics,   37 (2006),   no. 5, 265-272  (with P.K.Jain and S.K. Kaushik)     MR2271627,     Zbl 1125.46013. 

64.  On perturbation of Banach frames,   International Journal of Wavelets,  Multiresolution  and  Information  Process ,   4  (3) (2006),  559--565. (with P.K.Jain and S.K. Kaushik)  MR2260842,   Zbl 1213.42113. 

65.  Bessel sequences and Banach frames in Banach spaces,  Bulletin of  the  Calcutta Mathematical  Society,  98  (1) (2006),   87--92.(with P.K.Jain and S.K.Kaushik)  MR2218227. 

66.  Banach frames for conjugate Banach spaces,   Zeitschrift  fur Analysis und ihre  Anwendungen,   23  (4) (2004),  713--720. (with P.K.Jain and S. K. Kaushik)  MR2110399,   Zbl1059.42024.

67.  Some remarks in the theory of frames in Banach spaces,   Journal of  Analysis and  Applications,  2  (1) (2004),   39--50.  (with P.K.Jain and S.K.Kaushik). MR2038296,   Zbl1090.42019.

Conference Papers   

1. Construction of non-uniform Parseval wavelet frames for L^(R)  via UEP, In:  Proceedings of  Sampling Theory and Applications ( SampTA)   (2019),  1-3 pp (with  H.K. Malhotra). Published by the IEEE.    DOI:10.1109/SampTA45681.2019.9030867

2. Matrix-valued wave packet Bessel sequences and symmetric frames in  L^2(R^d, C^(s x r)),  In:  Proceeding  of the  International Workshop on Wavelets, Frames and Applications ( IWWFA) III- 2017,  organized by Department of Mathematics, Kirori Mal College, University of Delhi.  Published by  the  Poincare Journal of  Analysis and  Applications  (Special Issue) ,  2018 (2) , 77-96 . (with Jyoti, G.  Verma, and Virender) .  MR3903014,   Zbl 07084690.

3. On weaving fusion frames for Hilbert spaces, In:  Proceedings of  Sampling Theory and Applications ( SampTA)  (2017),  381-385 (with Deepshikha, S. Garg and G. Verma). Published by the IEEE.    DOI: 10.1109/SAMPTA.2017.8024363. 

4. On perturbation of local atoms for subspaces,  In:  Proceeding  of the  International Workshop on Wavelets, Frames and Applications ( IWWFA) II - 2014,  organized by Department of Mathematics, Kirori Mal College, University of Delhi.  Published by  the  Poincare Journal of  Analysis and  Applications  (Special Issue) , 2  (2015),  129-137.  (with Deepshikha)  MR3439947,  Zbl 1352.42040 .

5. On various types of frames in Banach spaces,  Proceeding  of the National Conference on Mathematics of soft computing,  National Institute of Technology (NIT), Calicut,  (2012), 109-112.

6. On weighted Banach frames,   In:  Proceeding  of the  International Workshop on Wavelets, Frames and Applications ( IWWFA) I- 2011,  organized by Department of Mathematics, Kirori Mal College, University of Delhi.  Published in the Communications in  Mathematics and  Applications,  (Special Issue) 3 (2012), 283-292 (with Shalu Sharma) .

7. On frames in Banach spaces,  In:  Proceeding  of the  International Workshop on Wavelets, Frames and Applications ( IWWFA) I- 2011,  organized by Department of Mathematics, Kirori Mal College, University of Delhi.  Published in Communications in  Mathematics and  Applications, (Special Issue) 3 (2012), 313-332.

Research Guidance

(I)      Ph.  D. 

 The following scholars have completed and got  the Ph. D. Degree

1.  Geetika Khattar.   Thesis Title: '' On the Reconstruction Property  and Frames in Banach Spaces '' .  Currently, Lecuter (ECDF),  Early Career Development Fellow- Cybersecurity/Mathematics,  STEM College,  School of Science,  RMIT University ,  Melbourne,   Australia.                                       

2.  Saakshi Garg.   Thesis Title: '' Weaving Generalized Frames in Hilbert Spaces and Frames in Locally Convex Spaces ''.    Currently, Assistant Professor in a college affiliated to the University of Delhi.                                                                           

3.  Deepshikha.   Thesis Title: '' Weaving Frames in Hilbert Spaces '' .   Currently,  Assistant Professor in a  Govt. college affiliated to the  Calcutta University.  

4.  Jyoti,  Thesis Title:  '' Matrix-Valued Wave Packet Frames ''.   Currently,  PostDoc Work.

5.  Hari Krishan Malhotra .   Thesis Title:  '' Nonuniform Wavelet  Frames and Nonuniform Multiresolution Analysis ''.   Currently,  Assistant Professor, MIT Pune.    

6.  Uttam Kumar Sinha.   Thesis Title:   '' Matrix-Valued  Gabor Frames  over Locally Compact  Groups '' .  Currently,  Assistant Professor,  Shivaji College,  University of Delhi.      

7.  Divya Jindal.   Thesis Title:   ''Frames  with  Several  Generators'' .  Currently,  Assistant Professor,   in a college affiliated to the IP University.                                           

The following scholars are currently  doing Ph. D.  

1. Manisha Chillar  (Under Progress).

2. Ruchi (Under Progress).

(II)      Postdoctoral Students 

 The following scholars are under PostDoc Fellowship

1.  Jyoti,   Project title: Hilbert-Schmidt Frames and Applications,  under the WISE-PDF research grant of WISE--KIRAN Division, Department of Science and Technology (DST), Government of India.

(III)     M. Phil.

The following scholars have completed and  got the M. Phil. Degree

1. Ashok  Kumar  Sah.  Dissertation Title: "A Study of  Irregular Weyl-Heisenberg Frames".  Currently,  Assistant Professor, in a college affiliated to the University of Delhi.  

2. Sah Jahan.   Dissertation Title: "Modular Frames  and Riesz Bases in Hilbert C*-Modules".  Currently,  Assistant Professor, Department of Mathematics, Central University of Haryana, Haryana.

3. Salaj.  Dissertation Title:  "A Study of Finite Frames in Hilbert Spaces " . Currently, Assistant Professor in a college affiliated to the  Maharishi Dayanand University, Rohtak.  

4. Sulbha Kumar   Dissertation Title:  '' Geometric Means of  Positive Definite Matrices'' (jointly with Tanvi Jain)

5. Soni.    Dissertation Title:  ''Wavelet Frames and Multiresolution Analysis on Local Fields '' . Currently, Assistant Professor in a college affiliated to the University of Delhi.  

6. Neha Sharma.   Dissertation Title:   ''Duality of Generalized Frames in Hilbert Spaces''.

7. Rajni Gupta.   Dissertation Title: ''Fusion Frames in Hilbert  Spaces''. Currently, Assistant Professor in a college affiliated to the University of Delhi.  

8. Ram Kishan  Dissertation Title:  ``Clarkson-McCarthy Inequalities  in C_p''.

Conference Participation

 Invited Talk 

1.  Delivered  a talk  entitled ''Duffin and Schaeffer inequality: Frames'' in the 91st Annual  Conference of Indian Mathematical Society (IMS) organized by  Department of Mathematics & Astronomy, University of Lucknow, Lucknow  during December 26--29, 2025.

2. Delivered  a talk  entitled "Frames of Nonuniform Wavelet Systems"  in the workshop on  Applied Matrix Positivity  (Online mode)  organized by the Internal Centre for Mathematical Sciences  (ICMS),  The Bayes Centre,  47 Potterrow,   Edinburgh,   during  July 19-23,   2021.

3. Delivered an invited talk  entitled ''Matrix-valued  Frames for Operators  in Matrix-valued Signal Spaces' in  the  International   Conference on  Analysis, Algebra, Combinatorics  and their Applications  organized by   Department of Mathematics, Jadavpur University, Kolkata during January  20-22, 2020. 

4. Delivered an invited talk  entitled ''Duality Principles in Wavelet Analysis' in a National  Conference on Advances in Mathematical Analysis and its Applications,  organized by   Department of Mathematics , PGDAV College, University of Delhi,   during  November 08--10 ,  2019.

5. Delivered a talk  entitled ''Woven Fusion Frames in Separable Hilbert Spaces' in a National  Conference on Recent Trends in  Mathematics  jointly organized by Bharata Ganita Parisad  and  Department of Mathematics & Astronomy, University of Lucknow, Lucknow  during  November 10-11 ,  2018.

6. Delivered an invited lecture entitled ''Hilbert Frames: A Signal Processing Prospective'' in International Conference on Applicable Mathematics organized by Department of Mathematics, Motilal Nehru College, University of Delhi, Delhi during 19-20 February, 2018.

7. Delivered an invited lecture entitled "The Reconstruction Property of Fractals  in L^p Spaces" in International workshop on wavelets, frames and applications III at Kirori Mal college, University of Delhi, Delhi during 14-20 December 2017.

8. Delivered an invited talk entitled '' Weaving Properties of Generalized Frames in Hilbert Spaces'' in International Conference  on Applicable Analysis, organized by Department of Mathematics, Shaheed Bhagat Singh College,University of Delhi, Delhi  during 08-11 February, 2017.

9. Delivered an invited talk entitled '' Discrete Frames of Translates in  C^N'' in National workshop on Analysis, Differential equations & Applications, at Department of Mathematics & Statistics, M. L. Sukhadia University, Udaipur (Raj.) during 25-27 February, 2016.

10. Delivered an invited lecture entitled " On Wave Packet Frames in L^2(R)" in International workshop on wavelets, frames and applications II at Kirori Mal college, University of Delhi, Delhi during 24-30 December 2014.

11. Delivered an invited lecture entitled " On Retro Banach Frames in  Banach spaces'' in National Conference on Recent Advances in Mathematics at Department of Mathematics & Astronomy, University of Lucknow, Lucknow during 2-4 February, 2012.

Talks in FDP 

1.  Delivered  a talk  entitled "Application of the Lipschitz condition in the Initial-Value Problem"  in the  Refresher course in Mathematical Sciences  (online mode) organized by the UGC  Malavia Mission Teacher Training  Centre, Aligarh Muslim University  during  December 10-23, 2025.

2.  Delivered  a talk  entitled "Generalized Hamel Bases in C^n"  in the  Refresher course on Innovations through mathematics: Practical Insights and Applications  (online mode) organized by the Department of Mathematics, University of Rajasthan, Jaipur during  December 01-13, 2025.

3.  Delivered  a talk  entitled "Schauder Bases in Banach Spaces"  in the  Refresher course on Mathematics/Operational Research/Statistics and Computer Science    (IDC)  (Online mode) on the theme “Mathematics with an Emphasis on Topology, Analysis and Applications”  organized by the Centre for Professional Development in Higher Education (CPDHE), UGC-HRDC, University of Delhi during September 2-15,  2022.

4. Delivered  a talk  entitled "The Matrix Exponential"  in the  Refresher course on Mathematics/Operational Research/Statistics and Computer Science    (IDC)  (Online mode) on the theme “Mathematics with an Emphasis on Topology, Analysis and Applications”  organized by the Centre for Professional Development in Higher Education (CPDHE), UGC-HRDC, University of Delhi during September 2-15,  2022. 

5. Delivered  a talk  entitled "Frames in Hilbert Spaces:  An Introduction"  in the  short term course on Mathematical Analysis and Applications  organized by the  Department of Mathematics,  Indian Institute of Technology (IIT) Roorkee during July 4-08,  2016,

6. Delivered  a talk  entitled "The Art of Frames"  in the  Refresher course on Mathematics/Operational Research/Statistics and Computer Science   organized  by  the Centre for Professional Development in Higher Education (CPDHE), UGC-HRDC, University of Delhi during  January  02-22,  2013.          

Paper Presentation

1. Present a paper entitled ''An application of  finite sums  of frames to the frame algorithm '' in  the National Conference on Applications of Mathematical  Tools  in Social Sciences  and Sciences (Online) ,  organized by Zakir Husain Delhi College, University of Delhi, during October 17-18, 2020,

2. Present a paper entitled ''Excess of Frames in Banach Spaces'' in  67th  Annual  conference Bharat Ganita Parishad,  conference on Modern Analysis & Applications-An International Meet organized by Department of Mathematics & Computer Science,  BBD University,  Lucknow during November 16-17, 2019.

3. Present a paper entitled '' Weaving Frames in Measure Spaces'' in International  conference on Recent Advances in Pure and Applied Mathematics & 28th Annual Conference of Rajastha Ganita Parishad, at Department of Mathematics & Statistics, M. L. Sukhadia Univesity, Udaipur (Raj.), during 13-14 February,  2017. 

4. Delivered  a talk "Extension of Bessel Systems to Frames in L^2(R)" in Conference on Geometry of Banach spaces and Operator Theory (GBOT) at IIT Kanpur  during 26 - 29 March,  2015.

5. Present a paper entitled "Some types of linear combinations of wave packet system in L^2(R)" in National conference on emerging trends in mathematical sciences organised by Department of Mathematics, Chaudhary Devi Lal University,  Sirsa  (Haryana) during March 17-18, 2015.

6. Present a paper entitled " Frames for subspaces in a discrete signal space" in National conference on Applications of Mathematics in Engineering and Sciences (AMES- 2014)  organised by Department of Mathematics, Motilal Nehru National Institute  of Technology (MNNIT) Allahabad, during November-29-30, 2014.

7. Present a paper entitled " On (\omega, \mu)-frames in Hilbert spaces, in National conference on Mathematics (NCOM-2013) organised by  department of Mathematics & Astronomy, University of Lucknow, Lucknow, during  29-11-2013  - 01-12-2013.

8. Present a paper entitle "On duality of retro Banach frames"  11th Biennial conference of ISIAM at Gautam Buddha University, Greater Noida during Dec. 15-16, 2012.Present a paper entitled " The Dynamics of Banach frames " in National Conference on Advances in Mathematical Sciences (AMS 2012), at Motilal Nehru National Institute of Technology, Allahabad, during October 05-07, 2012.

9. Present a paper entitled " On Various Types of Frames in Banach Spaces"  in National Conference on Mathematics  of Soft Computing at N I T Calicut, Kerla, during 05-07 July-2012.

10. Present a paper entitled " On Banach Frames II " in International  Workshop Wavelets, Frames and Applications at Kirori Mal College,University of Delhi during December 15-21,  2011.

  Organized  Conferences/Symposiums / Seminars

• 1.  Organized    ''National Research Scholars' Seminar'', Department of Mathematics, University of Delhi on December 28, 2018. 

  2. Organized a  Symposium on ''Frames and Wavelets '' in the 33rd Annual Conference of Ramanujan Mathematical Society in the  Department of Mathematics,           University of Delhi during June  01-03, 2018.

  3.  Organized  ''Research Scholar Seminar & Annual Conference of the Society of Mathematical Sciences (Delhi)'' in the Department of Mathematics, University of  Delhi during   May 01-02,  2017.

  4.  Organized ''National Conference on Algebra, Analysis, Coding and Cryptography" in honor of Prof. Bal Kishan Dass on the occasion of  his retirement in the                   Department of Mathematics, University of Delhi during  October 14-15, 2016.

  5.  Organized    ''Research Scholar Seminar'', Department of Mathematics, University of Delhi during  February 23-24, 2015.

Editorship 

1.  International Journal of Wavelets Multiresolution  and  Information  Processing  (IJWMIP).

    2.  Mathematical Journal of Interdisciplinary Sciences. 

Courses Taught

U G Level: Real Analysis;  Calculus;  Metric Space;  Linear Algebra;  Group Theory;   Ring Theory;  Mechanics;  Biomathematics;  Differential Equations;   Partial Differential Equations.

P G Level:  Functional Analysis;  Complex Analysis;   Matrix Analysis;   Fourier Analysis;  Measure & Integration; General Measure Theory;  Frames & Wavelets; Theory of Bounded Operators;  Operators on Hardy-Hilbert Spaces.

M.Phil. / Ph.D. Coursework: Advanced Frame Theory;  Research Methodology.