Books and Students

Editorship

  1. Methods of Functional Analysis in Approximation Theory, Proceedings of the International Conference at I.I.T. Bombay in December 1985, 410 pp., Birkauser Verlag, Basel, 1986 (with C.A. Micchelli and D.V. Pai).

Books

  1. Text Book of Mathematical Analysis, Tata McGraw-Hill Publishing Co. Ltd., New Delhi, ix + 214 pp., 1980 (Reprinted 2 times) (with other coauthors).

  2. Functional Analysis, Wiley Eastern Ltd., New Delhi, xii + 376 pp., 1981 (Reprinted 7 times).
  3. Second Edition, New Age International Ltd., New Delhi, x + 612 pp., 1996 (Reprinted 17 times).
    Third Edition, New Age International Ltd., New Delhi, x + 612 pp., 2014.
    Revised Third Edition, New Age International Ltd., New Delhi, x + 612 pp., 2017.

  4. Spectral Perturbation and Approximation with Numerical Experiments, Proceedings of the Centre for Mathematical Analysis, Vol. 13, Australian National University, Canberra, iv + 418 pp., 1987.

  5. Real Function Algebras, Marcel Dekker Inc., New York, v + 186 pp., 1992 (with S.H. Kulkarni).

  6. Spectral Computations for Bounded Operators, Applied Mathematics, Vol. 18, Chapman & Hall/CRC, Boca Raton, xvii + 382, 2001 (with M. Ahues and A. Largillier).

  7. A Course in Calculus and Real Analysis, Undergraduate Texts in Mathematics, Springer, New York and Springer (India), New Delhi, x + 432 pp., 2006 (with S. R. Ghorpade).

  8. A Course in Multivariable Calculus and Analysis, Undergraduate Texts in Mathematics, Springer, New York and Springer (India), New Delhi, xii + 475 pp., 2010 (with S.R. Ghorpade). (One of the top 25% most downloaded eBooks in the relevant Springer eBook Collection in 2013, 2014, 2015 and 2016)

  9. Linear Functional Analysis for Scientists and Engineers,[Our new book on multivariable calculus] Springer, Singapore, xiv + 254 pp., 2016


Supervision

Ph.D.
 
1979 
Sharad S. Sane
Studies in Partial Designs and Projective Hjelmslev Planes (Cosupervisor: G.A. Patwardhan)
1979
Sudhir H. Kulkarni
Some  Problems in Real Banach Algebras
1981
M.N. Narayanan Namboodri
Approximation by Positive Maps on Normed Algebras
1982
Rekha P. Kulkarni
Convergence and Computation of Approximate Eigenvalues
1986
M. Thamban Nair
Approximation and Localization of Eigenelements
1987
Lalita N. Deshpande
Approximate Solution of Eigenvalue Problems (Cosupervisor: M.V. Deshpande)
1996
Rafikul Alam
Accelerated Spectral Approximation (Cosupervisor: Rekha P. Kulkarni)
2013
Akshay S. Rane
Asymptotic Error Analysis of Numerical Solutions (Supervisor: Rekha P. Kulkarni)

M. Phil.
 
1998
Sarita S. Nemani
Spetral Approximation Theory for Variational Problems (Cosupervisor: Rekha P. Kulkarni)
2006
Harish V. N.
Approximate Solutions of Fredholm Integral Equations  (Cosupervisor: Rekha P. Kulkarni)

M.Sc.
 
1976
Sudhir H. Kulkarni
The Gelfand-Mazur Theorem and The Spectral Radius Formula for Normed Algebras
1977
Rekha P. Kulkarni
The Gelfand-Naimark Theorems for Real Banach Algebras
1981
Anilkumar S. Vaidya
On the Relative Roles of Real and Complex Numbers
1982
Lalita N. Deshpande
Computations of Eigenvalues of Large Matrices and Integral Operators by Iteration
1983
Cherian Varughese
Operators Methods in Quantum Mechanics
1988
Shaikh Mohammad Wajid
Iterative Refinement of Eigenelements
1995
N. Mahesh
Perturbation Techniques in Matrix Eigenvalue Problems
1996
Neelam Dogra
Spectral Approximation Theory
2000
Rekha Santhanam
Approximate Solutions of Operator Equations
2003
Megha Kumar
Some Results on Fixed Points
2006
Koushik Saha
Properities of Real-Valued Functions from a Geometric Point of View
2009
Shobhan Mandal
Monotonicity of Functions of Several Variables