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Major Areas: Operator Theory / Functional Analysis / Linear Algebra / Statistics
Generalized Inverses – Moore-Penrose, Core, Drazin inverses
Non-negativity of Generalized Inverses
Perturbed Systems & Operator Equations
Partial Orders on Matrices and Operators on Hilbert Spaces
Matrix Analysis - Inverse-positivity, Non-negativity
Applications of Generalized Inverses, Moore-Penrose Inverses and Non-negative Matrices
Linear Preserver Problems, Linear Complementarity Problems
Computation of Moore-Penrose Inverses
Image Processing (Deblurring, Denoising with Generalized Inverses)
Harmonic Analysis - Phase Retrieval, Phaseless Reconstruction, Norm Retrieval
Statistics, Biostatistics
Publications:
Shani Jose, K. C. Sivakumar. Moore-Penrose inverse of perturbed operators on Hilbert spaces. Proceedings of the International Workshop and Conference on Combinatorial Matrix Theory and Generalized Inverses of Matrices (CMTGIM 2012), Manipal, India. (Bapat, Ravindra B.; Kirkland, Steve J.; Prasad, K. Manjunatha & Puntanen, Simo (Eds)). Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer, 2013.
Shani Jose, K. C. Sivakumar. On inverse-positivity of sub-direct sums of matrices. Linear Algebra and Applications, Volume 439, Number 6, pp. 1670-1677, 2013.
Shani Jose, K. C. Sivakumar. On nonnegative Moore-Penrose inverses of perturbed matrices. Journal of Applied Mathematics, Volume 2013, Article ID 680975, 7 pages, 2013.
Shani Jose, K. C. Sivakumar. On partial orders of Hilbert space operators. Linear and Multilinear Algebra, Volume 63, Number 7, pp. 1423-1441, 2015.
Shani Jose, K. C. Sivakumar. Sub-direct sum of operators on Hilbert spaces and nonnegative Moore-Penrose inverses. Acta Sci. Math. (Szeged), Volume 81, pp. 215-240, 2015.
V. B. S. Prasath, D. Vorotnikov, R. Pelapur, Shani Jose, G. Seetharaman, K. Palaniappan. Multiscale Tikhonov-total variation image restoration using spatially varying edge coherence exponent. IEEE Transactions on Image Processing, Volume 24, Number 12, pp. 5220-5235, 2015. (Project)
Peter Casazza, Dorsa Ghoreishi, Shani Jose, Janet Tremain. Norm retrieval and phase retrieval by projections. Axioms, Special issue on Wavelet and Frame Constructions, with Applications, Volume 6, Number 1, 6, March 2017.
Sara Botello-Andrade, Peter G. Casazza, Dorsa Ghoreishi, Shani Jose, Janet C. Tremain. Weak phase retrieval and phaseless reconstruction. ArXiv:1612.08018, 2016.
Sara Botello-Andrade, Peter G. Casazza, Dorsa Ghoreishi, Shani Jose, Janet C. Tremain. Weak phase retrieval. Compressed Sensing and Its Applications (Eds. H. Boche et al), Applied and Numerical Harmonic Analysis, Springer, 2018.
PhD Thesis
Shani Jose. Moore-Penrose Inverses of Sums, Sub-direct Sums and Applications. PhD Thesis, Department of Mathematics, Indian Institute of Technology Madras, India. Submitted July 2013. Defended March 2014.
MPhil Thesis
Shani Jose. A Study on Toeplitz matrices Through Circulants. MPhil Thesis, Department of Mathematics, Cochin University of Science and Technology (CUSAT), India. September 2008.
Talks:
"Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces and their Nonnegativity", on March 18, 2013, Research Seminar Talk - I, Department of Mathematics, Indian Institute of Technology Madras (IITM), India.
"Sub-Direct Sums of Operators", on May 15, 2013, Research Seminar Talk - II, Department of Mathematics, Indian Institute of Technology Madras (IITM), India.
"On Inverse-Positivity of Sub-direct Sums of Matrices", International Linear Algebra Society Meeting (ILAS), June 3 - 7, 2013, Providence, RI, USA. (Talk Slides)
"Moore-Penrose Inverses of Perturbed Operators on Hilbert Spaces", Prairie Analysis Seminar, September 27 - 28, 2013, Department of Mathematics, Kansas State University, Manhattan, KS, USA. (Talk Slides)
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