My broad fields of interest are

Functional Analysis and Numerical Analysis.

More specifically, I have worked in

Banach Algebras, Operator Theory, Generalized

Inverses of Linear Operators and their appications to Optimization Problems.

You can have a look at my published and reviewed papers with links to the reviews by

clicking here.

Some details about my academic background are given in my curriculum vitae.

This page is still under construction. I hope to be able to put complete articles

on this page. Meanwhile here are a few things.

Books

Articles

Invited talks

Courses

Supervision

- Kulkarni, S. H.; Limaye, B. V. Real function algebras.

Monographs and Textbooks in Pure and Applied Mathematics, 168.

Marcel Dekker, Inc., New York, 1992. viii+186 pp. ISBN: 0-8247-8653-X

MR 1197884### Edited Proceedings

- Kulkarni Rekha P.; Kulkarni S. H.; Filomina D. d'Almeida; Pani A. K.

(Editors) Proceedings of the International Conference on

Topics in Functional and Numerical Analysis(TOFNA-05)

held at the Indian Institute of Technology Bombay, December 7-9, 2005.

Journal of Analysis, Volume 14 (2006). - Agrawal Sushama; Kulkarni S. H.; Rao T. S. S. R. K. (Editors) Proceedings of the

Eleventh Ramanujan Symposium on Recent Trends in Operator Theory and Banach Algebras

held at Ramanujan Institute of Advanced Study in Mathematics Chennai, March 3-5, 2004.

Journal of Analysis, Volume 12 (2004). - Kulkarni, S. H.; Namboodiri, M. N. N. (Editors) Proceedings of the

International Workshop on Linear Algebra, Numerical Functional Analysis and Wavelet Analysis

held at Cochin University of Science and Technology, Kochi, August 6-15, 2001.

Allied Publishers, Chennai, 2003. ISBN: 81-7764-506-4 MR 2094086

A more detailed list can be found here.

- Kulkarni, S. H.; Nair; M. T.; Ramesh, G.

Some properties of unbounded operators with closed range

To appear in the Proc. Indian Acad. Sci. Math. Sci.

View complete article. - Kulkarni, S. H.; Sukumar, D.

Condition spectrum

To appear in Acta Sci. Math.(Szeged)

View complete article. - Kulkarni, S. H.; Radha, R.; Sivananthan, S.

Nonuniform Sampling Problem

To appear in Journal of Functional Analysis and Applications

View complete article. - Kulkarni, S. H.; Ramesh, G.

Projection Methods for Inversion of Unbounded Operators

Indian J. Pure Appl. Math. 39 (2008) no. 2, 185 -- 202.

View complete article. - Kulkarni, S. H.

A relatively elementary proof of a characterization of polynomials.

Indian J. Pure Appl. Math. 38 (2007), no. 4, 229--230. 2349286

View complete article. - Balasubramanian, R.; Kulkarni, S. H.; Radha, R.

Solution of a tridiagonal operator equation.

Linear Algebra Appl. 414 (2006), no. 1, 389--405. (Reviewer: Stefano Serra Capizzano) MR 2210215

View complete article. - Kulkarni, S. H.; Nair, M. T.; Namboodiri, M. N. N.

An elementary proof for a characterization of $\sp *$-isomorphisms.

Proc. Amer. Math. Soc. 134 (2006), no. 1, 229--234. (Reviewer: Borut Zalar) MR 2170562

View complete article. - Kulkarni, S. H.; Sukumar, D.

Gleason-Kahane-\.Zelazko theorem for spectrally bounded algebra.

Int. J. Math. Math. Sci. 2005, no. 15, 2447--2460. (Reviewer: Krzysztof Jarosz) MR 2184484

View complete article. - Kulkarni, S. H.; Sivakumar, K. C.

Three types of operator monotonicity.

J. Anal. 12 (2004), 153--163. (Reviewer: A. M. Galperin) MR 2145774 - Agrawal, Sushama; Kulkarni, S. H.

Spectral theorem for an unbounded normal operator in a real Hilbert space.

J. Anal. 12 (2004), 107--114. MR 2142967 - Kulkarni, S. H.

A very simple and elementary proof of a theorem of Ingelstam.

Amer. Math. Monthly 111 (2004), no. 1, 54--58. 46H05 (17A80 46K05) MR 2026316

View complete article. - Balasubramanian, R.; Kulkarni, S. H.; Radha, R.

Finite dimensional approximations of the operator equations. Linear algebra, numerical functional analysis and wavelet analysis, 57--64, Allied Publ., New Delhi, 2003. 47A50 (47B36) MR 2095238

View complete article. - Balasubramanian, R.; Kulkarni, S. H.; Radha, R.

Non-invertibility of certain almost

Mathieu operators.

Proc. Amer. Math. Soc. 129 (2001), no. 7, 2017--2018 (electronic). 47A05 (47N50) MR 1825912

View complete article. - Agrawal, Sushama; Kulkarni, S. H.

An analogue of the Riesz-representation theorem.

Novi Sad J. Math. 30 (2000), no. 1, 143--154. MR1835639 (2002g:46036) MR 1835639

View complete article. - Agrawal, Sushama; Kulkarni, S. H.

Dual spaces of quaternion normed linear spaces

and reflexivity. J. Anal. 8 (2000), 79--90. MR1806397 (2001k:46013) 1806397 -
Kulkarni, S. H.

Arzela-Ascoli theorem is stable.

Internat. J. Math. Ed. Sci. Tech. 31 (2000), no. 6, 919--922. MR1799409 1799409

A little longer list of invited talks can be found here.

- Banach algebras (six lectures), Indian Statistical Institute Bangalore, June 2008.
- Condition spectrum, I.I.T. Bombay, February 28, 2008. View complete article.
- Projection methods and unbounded operators, Scott Christian College, Nagercoil, November 30, 2007. View complete article.
- Frames and generalized inverses (two lectures), B.H.U. Varanasi, October 25/26, 2007.
- Teaching of Functional Analysis, N.I.T. Karnataka, Suratkal, June 7, 2007.
- Spectral Theorem (four lectures), Ramanujan Institute of Advanced Studies in Mathematics, Chennai, June, 2007.
- Fourier series in Hilbert spaces (four lectures), Ramanujan Institute of Advanced Studies in Mathematics, Chennai, November, 2007.
- What does the Singular Value Decomposition Theorem say?

Ramanujan Endowment Lecture, Anna University, chennnai, January 31, 2007. - Projection methods for solving operator equations. ,

Burdwan University, January 7, 2007. - Some generalizations of the spectrum of an element in a Banach algebra.

I.I.T. Madras, December 22, 2006. - An elementary proof of a characterization of polynomials.

Vivekananda College, Chennai, March 29, 2006. View complete article. - An elementary proof of characterization of *-isomorphisms.

N.S.S. College Ottapalam, March 18, 2006. View full article. - Condition spectrum and some of its properties.

Cochin University of Science and Technology, March 16, 2006. View complete article. - Condition spectrum of an element in a Banach algebra.

I.I.Sc. Bangalore, December 19, 2005. View complete article. - Uniform norms on real algebras.

I.I.T. Bombay, December 9, 2005.

- MA 101: Elements of Calculus
- MA 215: Linear Algebra and Optimization

A complete list of all the courses that I have taught so far can be found here.

- G. Ramesh, APPROXIMATION METHODS FOR SOLVING OPERATOR EQUATIONS INVOLVING UNBOUNDED OPERATORS, 2008.
- D. Sukumar, RANSFORD SPECTRUM IN BANACH ALGEBRA, 2007.
A complete list can be found here.