Embedded Files
Book:
B V Rajarama Bhat and Tirthankar Bhattacharyya, Dilations, Completely Positive Maps and Geometry, Indian edition by Hindustan Book Agency, 2023. International edition by Springer, 2023. Available on Amazon.
Books edited:
T. Bhattacharyya, M. A. Dritschel (Eds.), Operator Algebras and Mathematical Physics, Operator Theory: Adv. and Appl., Vol. Nr. 247, Springer Basel AG, Basel, 2015.
T. Bhattacharyya, R. A. Horn and T. S. S. R. K. Rao (Eds.), In the matrix mould, Expository articles by Rajendra Bhatia. Hindustan Book Agency, New Delhi, 2013.
Papers:
59. Gromov-Hausdorff convergence of metric spaces of UCP maps, co-authored with Ritul Duhan and Chandan Pradhan. Journal of Geometry and Physics. DoI is 10.1016/j.geomphys.2025.105588 and arXiv identifier is arXiv:2410.15454.
58. Hankel operators and projective Hilbert modules on quotients of bounded symmetric domains, co-authored with Mainak Bhowmik and Haripada Sau. arXiv identifier is arXiv:2409.04582.
57. Complete Nevanlinna-Pick Kernels and the Curvature Invariant, co-authored with Abhay Jindal. Annali di Matematica Pura ed Applicata (2024). DoI is 10.1007/s10231-024-01524-1 and arXiv identifier is 2401.15591.
56. Lipschitz Estimates and an application to trace formulae, co-authored with Arup Chattopadhyay, Saikat Giri and Chandan Pradhan. Banach Journal of Mathematical Analysis. DOI is 10.1007/s43037-025-00454-1 and arXiv identifier is 2312.08706.
55. Complete Nevanlinna-Pick kernels, the Schwarz lemma and the Schur algorithm , co-authored with Daniel Alpay, Abhay Jindal and Poornendu Kumar. Complex Variables and Elliptic Equations. DOI is 10.1080/17476933.2025.2454683 arXiv identifier is 2312.01287.
54. Functions with image in a strip, co-authored with Anthony G. O’Farrell, Shubham Rastogi and U. Vijaya Kumar. Infin. Dimens. Anal. Quantum Probab. Relat. Top. (2024) Paper no. 2440008. arXiv identifier is 2406.02901.
53. On Herglotz's representation and Caratheodory's approximation, co-authored with Mainak Bhowmik and Poornendu Kumar. Bull. Lond. Math. Soc. (2024) DOI is 10.1112/blms.13165 and arXiv identifier is 2311.1556852.
52. Kernels with complete Nevanlinna-Pick factors and the characteristic function, co-authored with Abhay Jindal. To appear in the Journal of Operator Theory and arXiv identifier is 2307.10595.
51. On factorization of the shift semigroup, co-authored with Shubham Rastogi, Kalyan Bidhan Sinha and Vijaya Kumar U. To appear in the Annals of Functional Analysis. arXiv identifier is 2306.15343.
50. Doubly commuting and dual doubly commuting semigroups of isometries, co-authored with Shubham Rastogi and Vijaya Kumar U. Journal of Operator Theory. DOI is 10.7900/jot.2023jan28.2425 and arXiv identifier is 2306.14183.
49. A note on the dilation of a certain family of tetrablock contractions, co-authored with Mainak Bhowmik. In: Ptak, M., Woerdeman, H.J., Wojtylak, M. (eds) Operator and Matrix Theory, Function Spaces, and Applications. IWOTA 2022. Operator Theory: Advances and Applications, vol 295. Birkhäuser, Cham. DOI is 10.1007/978-3-031-50613-0_4 and arXiv identifier is 2204.10753.
48. Sequences of operator algebras converging to odd spheres in the quantum Gromov-Hausdorff distance, co-authored with Sushil Singla. Indian J. Pure Appl. Math. 6 July, 2024. DOI is 10.1007/s13226-024-00635-y and arXiv identifier is 2211.04321.
47. A dilation theoretic approach to approximation by inner functions, co-authored with Daniel Alpay, Abhay Jindal and Poornendu Kumar. Bull. Lond. Math. Soc. DOI is 10.1112/blms.12897 and arXiv identifier is 2203.10936.
46. Complete Nevanlinna-Pick kernels and the characteristic function, co-authored with Abhay Jindal. Advances in Mathematics, Volume 426, 1 August 2023, 109089. DOI is 10.1016/j.aim.2023.109089 and arXiv identifier is 2110.00223.
45. On the structure and joint spectrum of a pair of commuting isometries , co-authored with Shubham Rastogi and Vijaya Kumar U, Complex Analysis and Operator Theory, (2022) 16:83. DOI is 10.1007/s11785-022-01257-0 and arXiv identifier is 2105.02134. The full text is also available for viewing at https://rdcu.be/cRWti.
44. On the geometry of the symmetrized bidisc, co-authored with A. Biswas and A. Maitra. Indiana Univ. Math. J., Volume 71 (2022), Issue 2, pages 685-713. DOI is 10.1512/iumj.2022.71.8896 and arXiv identifier is 2005.00289.
43. Distinguished Varieties Through the Berger--Coburn--Lebow Theorem, co-authored with P. Kumar and H. Sau, Analysis & PDE, Volume 15 (2022), Number 2, pages 477-506. DOI is 10.2140/apde.2022.15.477 and arXiv identifier is 2001.01410.
42. Toeplitz operators and Hilbert modules on the symmetrized polydisc , co-authored with B. Krishna Das and H. Sau. International Journal of Mathematics, (2022) 2250076. DOI is 10.1142/S0129167X22500768 and arXiv identifier is 2207.01285.
41. Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidisk, co-authored with H. Sau, Journal of Operator Theory, Volume 87 (2022), Issue 2, pp. 435-459. DOI is 10.7900/jot.2020oct07.2311 and arXiv identifier is 1909.03237.
40. Toeplitz operators on the symmetrized bidisc, co-authored with B. Krishna Das and H. Sau, International Mathematics Research Notices (IMRN), Volume 2021, Issue 11, June 2021, Pages 8763–8805. DOI is 10.1093/imrn/rnz333 and arXiv identifier is 1706.03463. This article has an Addendum whose DOI is 10.1093/imrn/rnab252.
39. Some thoughts on composition operators on subspaces of the Hardy space, co-authored with J. Anand and S. Srivastava, Archiv der Mathematik, 114 (2020), 431–444. DOI is 10.1007/s00013-019-01406-6.
38. On the Nevanlinna problem - Characterization of all Schur-Agler class solutions affiliated to a given kernel, co-authored with A. Biswas and V. Singh Chandel. Studia Mathematica, 255 (2020), 83-107 . DOI is 10.4064/sm190505-8-10 and arXiv identifier is 1905.04301.
37. Survey of last ten years of work done in India in some selected areas of functional analysis and operator theory, co-authored with T S R K Rao, Indian Journal of Pure and Applied Mathematics, September 2019, Volume 50, Issue 3, pp 599–617. DOI is 10.1007/s13226-019-0345-4 . Available online and free at https://www.insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/Vol50_2019_3_ART02.pdf
36. Holomorphic functions on the symmetrized bidisk -- realization, interpolation and Extension, co-authored with H. Sau, J. Funct. Anal. 274 (2018), 504-524. DOI is 10.1016/j.jfa.2017.09.013 and arXiv link is https://arxiv.org/pdf/1511.08962.pdf
35. Analytic model of doubly commuting contractions, co-authored with E. K. Narayanan and J. Sarkar, Oper. Matrices 11 (2017), no. 1, pages 101 - 113. DOI is 10.7153/oam-11-07 and arXiv link is https://arxiv.org/pdf/1310.0950.pdf
34. G -unitaries, dilation and a natural example, co-authored with H. Sau, Publ. Res. Inst. Math. Sci. 53 (2017), no. 2, pages 261 - 285. DOI is 10.4171/PRIMS/53-2-2 and arXiv link is https://arxiv.org/pdf/1311.1577.pdf
33. Explicit and unique construction of tetrablock unitary dilation in a certain case, co-authored with H. Sau, Complex Anal. Oper. Theory 10 (2016), no. 4, pages 749 - 768. DOI is 10.1007/s11785-015-0472-9 and arXiv link is https://arxiv.org/pdf/1412.4363.pdf
32. Admissible fundamental operators, co-authored with S. Lata and H. Sau, Journal of Mathematical Analysis and Applications 425 (2015), pages 983 - 1003. DOI is 10.1016/j.jmaa.2015.01.006 and arXiv link is https://arxiv.org/pdf/1404.5819.pdf
31. The tetrablock as a spectral set, Indiana Univ. Math. J. 63 (2014), no. 6, pages 1601 - 1629. DOI is 10.1512/iumj.2014.63.5407 and arXiv link is https://arxiv.org/pdf/1207.3395.pdf
30. A functional model for pure Gamma contractions, co-authored with S. Pal, Journal of Operator Theory 71 (2014), no. 2, pages 327 - 339. DOI is 10.7900/jot.2012mar21.1946 and arXiv link is https://arxiv.org/pdf/1202.3841.pdf
29. Characterization of Birkhoff-James orthogonality, co-authored with P. Grover, Journal of Mathematical Analysis and Applications 407 (2013), pages 350-358. DOI is 10.1016/j.jmaa.2013.05.022, open access
28. The Defect sequence for contractive tuples, co-authored with B. Krishna Das, S. Sarkar, Linear Algebra and Its Applications, 438 (2013), pages 315 - 330. DOI is 10.1016/j.laa.2012.07.041 and arXiv link is https://arxiv.org/pdf/1211.5898.pdf
27. Completely bounded kernels, co-authored with M. A. Dritschel and C. S. Todd, Acta Sci. Math. (Szeged), vol. 79, issues 1-2(2013), pages 191-217. DOI is not known, arXiv link is https://arxiv.org/pdf/1001.3590.pdf
26. Hilbert W* modules and coherent states, co-authored with S. Shyam Roy, Journal of Physics A: Math. Theor., vol. 45, 244020 (6pp), 2012. DOI is 10.1088/1751-8113/45/24/244020
25. Dilation of Gamma contractions by solving operator equations, co-authored with S. Pal and S. Shyam Roy, Advances in Mathematics, 230 (2012), pages 577 - 606. DOI is 10.1016/j.aim.2012.02.016 and arXiv link is https://arxiv.org/pdf/1108.0774.pdf
24. Coincidence of Schur Multipliers of the Drury-Arveson Space, co-authored with A. Bhattacharya, Acta Sci. Math. (Szeged), vol. 78, issues 1-2 (2012), pages 265-277. DOI is not known, the arXiv link is https://arxiv.org/abs/0911.3488
23. Abstract characteristic function, Complex Analysis and Operator Theory, vol. 6, issue 1, pages 91-103. DOI is 10.1007/s11785-010-0065-6
22. Coherent states on Hilbert modules, co-authored with S. T. Ali and S. Shyam Roy, Journal of Physics A, vol. 44, no. 27, 275202, 16 pages. DOI is 10.1088/1751-8113/44/27/275202 and the arXiv link is https://arxiv.org/pdf/1007.0798.pdf
21. Coherence of the real symmetric Hardy algebra, co-authored with A. Sasane, Operators and Matrices, vol. 5 no. 2, pages 303 - 308. DOI is 10.7153/oam-05-21
20. Complete Pick Positivity and Unitary Invariance, co-authored with A. Bhattacharya, Studia Mathematica, 200, pages 149-162. DOI is 10.4064/sm200-2-3 and the arXiv link is https://arxiv.org/abs/0910.5093
19. A learning algorithm for risk-sensitive cost, co-authored with A. Basu and V. S. Borkar, Mathematics of Operations Research, vol. 33, No. 4, pages 880-898. DOI is 10.1287/moor.1080.0324
18. On c.n.c commuting contractive tuples, co-authored with J. Eschmeier and J. Sarkar, Proc. Indian Acad. Sci., Math. Sci., vol. 116, no. 3, pages 299 - 316. DOI is 10.1007/BF02829747 and the arXiv link is https://arxiv.org/pdf/math/0509162.pdf
17. Contractive and completely contractive maps over planar algebras, co-authored with G. Misra, Illinois Journal of Mathematics, 49, no. 4, pages 1181 - 1201. Permanent link is projecteuclid.org/euclid.ijm/1258138134 and the arXiv link is https://arxiv.org/pdf/math/0505251.pdf
16. Two parameter uniformly elliptic Sturm-Liouville problems with eigenparameter dependent boundary conditions, co-authored with J. P. Mohandas, Proceedings of Edinburgh Mathematical Society, vol. 48, no. 3, pages 531--547. DOI is 10.1007/1-4020-2623-4_2
15. Characteristic function for polynomially contractive commuting tuples, co-authored with J. Sarkar, Journal of Mathematical Analysis and Applications, vol. 321, No. 1, pages 242 - 259. DOI is 10.1016/j.jmaa.2005.07.075
14. Characteristic function of a pure commuting contractive tuple, co-authored with J. Eschmeier and J. Sarkar, Integral Equations Operator Theory, vol. 53, no. 1, pp. 23 - 32. DOI is 10.1007/s00020-004-1309-5
13. Standard non-commuting and commuting dilations of commuting tuples, co-authored with B.V.R. Bhat and S. Dey, Transactions of American Math. Society, vol.356, No.4, pp. 1551 - 1568. DOI is 10.1090/S0002-9947-03-03310-5
12. Dilation of contractive tuples: a survey, Surveys in Analysis and Operator Theory, vol. 40, CMA, Australian National University, pp. 89 - 126, 2002.
11. Right definite multiparameter Sturm-Liouville problems with eigenparameter dependent boundary conditions, co-authored with T. Kosir and B. Plestenjak, Proceedings of Edinburgh Mathematical Society, vol. 45, pp. 565-578, 2002. DOI is 10.1017/S0013091501000207
10. Some thoughts on Ando's theorem and Parrott's example, co-authored with B. Bagchi and G. Misra, Linear Algebra and Its Applications, vol.341, pages 357-367, 2002. DOI is 10.1016/S0024-3795(01)00454-2
9. A model theory for q-commuting contractive tuples, co-authored with B.V. R. Bhat, Journal of Operator Theory, vol.47, pages 97-116, 2002. Stable URL: http://www.jstor.org/stable/24715527
8. Commuting compact self-adjoint operators on a Pontryagin Space, co-authored with T. Kosir, Integral Equations and Operator Theory, vol.39, pages 377-386, 2001. DOI is 10.1007/BF01203319
7. Multiparameter Sturm-Liouville problems with eigenparameter dependent boundary conditions, co-authored with P.A. Binding and K. Seddighi, Journal of Mathematical Analysis and Applications, vol.264, pages 560-576, 2001. DOI is 10.1006/jmaa.2001.7695
6. Two parameter right definite Sturm-Liouville problems with eigenparameter dependent boundary conditions, co-authored with P.A. Binding and K. Seddighi, Proceedings of Royal Society of Edinburgh Sect. A, vol. 131, pages 45-58, 2001. DOI is 10.1017/S0308210500000780
5. On finite-dimensional commutative non-hermitian fusion algebras, Linear Algebra and Its Applications, vol.287, pages 87-103, 1999. DOI is 10.1016/S0024-3795(98)10135-0
4. On tuples of commuting compact operators, Publications RIMS Kyoto Univ. vol. 32, no. 5, pages 785-795, 1996. DOI is 10.2977/prims/1195162382
3. On the joint spectral radius of commuting matrices, co-authored with R. Bhatia, Studia Mathematica, vol.114, pages 29-38, 1995. Online access at http://matwbn.icm.edu.pl/ksiazki/sm/sm114/sm11413.pdf
2. A generalization of the Hoffman-Wielandt Theorem, co-authored with R. Bhatia, Linear Algebra and Its Applications, vol. 179, pages 11-17, 1993. DOI is 10.1016/0024-3795(93)90318-I
1. A Henrici theorem for joint spectra of commuting matrices, co-authored with R. Bhatia, Proceedings of American Math. Society, vol.118 pages 5-14, 1993. Online access at http://www.ams.org/journals/proc/1993-118-01/S0002-9939-1993-1160292-7/S0002-9939-1993-1160292-7.pdf
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