# Papers in Journals/Proceedings

### Research Papers in Journals

#### Algebraic Analysis

1. Blaschke products for finite Riemann surfaces, Studia Mathematica (Poland), 34 (1970), 169-176.
2. On the inner parts of certain analytic functions, Annales Polonici Mathematici (Poland), 26 (1972), 295-304.
3. Ideal theory on non-orientable Klein surfaces, Arkiv fur Matematic (Sweeden), 10 (1972), 277-293 (with N.L. Alling).
4. Ahlfors functions on triply connected domains, J. Indian Math. Soc. (India), 37 (1973), 125-135.
5. Deficiencies of certain real uniform algebras, Canadian J. Math. (Canada), 27 (1975), 121-132 (with R.R. Simha).
6. Boundaries for real Banach algebras, Canadian J. Math. (Canada), 28 (1976), 42-49.
7. Gelfand-Naimark theorems for real Banach *algebras, Math. Japonica (Japan), 25 (1980), 545-558 (with S.H. Kulkarni).
8. Gleason parts of real function algebras, Canadian J. Math. (Canada), 33 (1981), 181-200 (with S.H. Kulkarni).
9. The spectral mapping theorem for real Banach algebras, Houston J. Math. (U.S.A.), 7 (1981), 507-517, (with S.H. Kulkarni).
10. Maximal ideal space and Silov boundary of the tensor product of real Banach algebras, Glasnik Matematicki (Croatia), 17 (1982), 277-283 (with R.D. Mehta and M.H. Vasavada).
11. A topological characterization of Gleason parts of real function algebras, Canadian Math. Bull. (Canada), 26 (1983), 44-49 (with S.H. Kulkarni).
12. Isometry of an analytic map onto a Gleason part, Glasnik Matematicki (Croatia), 21 (1986), 353-356 (with S.H. Kulkarni).
13. Extreme points of the unit ball in the dual spaces of some real subspaces of C(X), Glasnik Matematicki (Croatia), 29 (1994), 333-340 (with S.H. Kulkarni).
14. Boundaries and Choquet sets for real subspaces of C(X), Math. Japonica (Japan), 51 (2000), 199-212 (with S.H. Kulkarni).
15. A geometric approach to saddle points , Austral. Math. Soc. Gaz. (Australia), 36 (2009), 127-136 (with S.R. Ghorpade).
16. On the Pringsheim convergence of double series, Proc. Estonian Acad. Sc. (Estonia), 58 (2009), 108-121 (with M. Zeltser).

#### Projective Geometry

1. The fundamental theorem for the projective line over commutative rings, Acquationes Mathematicae (Canada), 13, (1977), 275-281 (with N.B. Limaye).
2. Fundamental theorem for the projective line over non-commutative local rings, Archive der Mathematik (Germany), 28 (1977), 102-109 (with N.B. Limaye).
3. On partial designs and m-uniform projective Hjelmslev planes, J. Combinatorics, Information and System Sciences (India), 3 (1978), 223-237 (with S.S. Sane).

#### Positive Approximation

1. Korovkin's theorem for positive functionals on *normed algebras, J. Indian Math. Soc. (India), 40 (1976), 163-172 (with S.D. Shirali).
2. Approximation by positive functionals, J. Indian Math. Soc. (India), 43 (1979), 195-202 (with M.N. Namboodiri).
3. Korovkin-type approximation on C*-algebras, J. Approximation Theory (U.S.A.), 34 (1982), 237-246 (with M.N. Namboodiri).
4. A generalized noncommutative Korovkin theorem and *-closedness of certain sets of convergence, Illinois J. Math. (U.S.A.), 28 (1984), 267-280, (with M.N. Namboodiri).
5. Weak Korovkin approximation by completely positive linear maps on \beta (H), J. Approximation Theory (U.S.A.), 42 (1984), p. 202-211 (with M.N. Namboodiri).
6. Weak approximation by positive maps on C*-algebras, Mathematica Slovaca (Slovakia), 36 (1986), 91-99 (with M.N. Namboodiri).

#### Approximate Solutions of Eigenvalue Problems and Operator Equations

1. On error bounds in strong approximation for eigenvalue problems, J. Australian Math. Soc. Series B (Australia), 22 (1981), 270-283 (with R.P. Kulkarni).
2. On the steps of convergence of approximate eigenvectors in the Rayleigh-Schrodinger series, Numerische Mathematik (Germany), 42 (1983), 31-50 (with R.P. Kulkarni).
3. Geometric and semigeometric approximation of spectral projections, J. Math. Analysis and Applications (U.S.A), 101 (1984), p.139-159 (with R.P. Kulkarni).
4. Localization of a simple eigenvalue and a corresponding eigenvector, Houston J. Math. (U.S.A.), 17 (1987), 129-141 (with M.T. Nair).
5. On the accuracy of the Rayleigh-Schrodinger approximations, J. Math. Analysis and Applications (U.S.A.), 138 (1989), 413-431 (with M.T. Nair).
6. On the error estimates for the Rayleigh-Schrodinger series and the Kato-Rellich Perturbation series, J. Australian Math. Soc. Series B (Australia), 46 (1989), 456-468 (with R.P. Kulkarni).
7. A fixed point technique to refine a simple approximate eigenvalue and a corresponding eigenvector, Numer. Funct. Anal. and Optimiz. (U.S.A.), 10 (1989), 909-921 (with L.N. Deshpande).
8. Solution of a Schrodinger equation by iterative refinement, J. Australian Math. Soc. Series B (Australia), 32 (1990), 115-132 (with R.P. Kulkarni).
9. Eigenelements of perturbed operators, J. Australian Math. Soc. Series A (Australia), 49 (1990), 138-148 (with M.T. Nair).
10. A note on iterative refinement schemes for Sylvester operator equations, Appl. Math. Lett. (U.S.A.), 6 (1993) 83-86 (with M. Ahues and A. Largillier).
11. Boundedness of adjoint bases of approximate spectral subspaces and of associated block reduced resolvents, Numer. Funct. Anal. and Optimiz. (U.S.A.), 17 (1996), 473-502 (with R. Alam and R.P. Kulkarni).
12. Accelerated spectral approximation, Math. Comp. (U.S.A.), 67 (1998), 1401-1422 (with R. Alam and R.P. Kulkarni).
13. Accelerated spectral refinement, Part I: Simple eigenvalue, J. Australian Math. Soc. Series B (Australia), 41 (2000), 487-507 (with R. Alam and R.P. Kulkarni).
14. Accelerated spectral refinement, Part II: Cluster of eigenvalues, ANZIAM J. (Australia), 42 (2000), 224-243 (with R. Alam and R.P. Kulkarni).
15. Computation of spectral subspaces for weakly singular integral operators, Numer. Funct. Anal. and Optimiz. (U.S.A.), 25 (2004), 1-14 (with M. Ahues).
16. A singularity subtraction iterative refinement scheme for spectral subspaces of weakly singular operators, J. Analysis (India), 16 (2006), 111-133 (with M. Ahues and A. Largillier).
17. Uniformly conditioned bases of spectral subspaces, Numer. Funct. Anal. and Optimiz. (U.S.A.), 34 (2013), 180-206.

#### Linear Algebra

1. On the stability of singular finite-rank methods, SIAM J. Numer. Anal. (U.S.A.), 27 (1990), 792-803 (with L.N. Deshpande).
2. On a spectral characterization of rank one matrices, Lin. Alg. and Appl. (U.S.A.), 143 (1991), 1-6 (with H. Deguang).
3. A spectral characterization of operators having rank k, Lin. Alg. and Appl. (U.S.A.), 143 (1991), 57-66.
4. On the multiplicities and the ascent of an eigenvalue of a linear map, Math. Student (India), 64 (1995), 162-166 (with M.T. Nair).
5. Finite-rank methods and their stability for coupled systems of operator equations, SIAM J. Numer. Anal. (U.S.A.), 33 (1996), 707-728 (with A. Largillier).
6. On error bounds for eigenvalues of a matrix pencil, Lin. Alg. and Appl. (U.S.A.), 268 (1998), 71-89 (with M. Ahues).
7. Sylvester's minorant criterion, Lagrange-Beltrami identity, and nonnegative definiteness, Math. Student (India), Special Centenary Volume (2007), 123-130 (with S.R. Ghorpade).
8. Matrix formulation for infinite-rank operators, Operators and Matrices (Croatia), 6 (2012), 357-370.
9. On condition numbers of a basis, Lin. Alg. and Appl. (U.S.A.), 439 (2013), 3359-3377 (with M. Ahues). (Listed among the Top 25 Hottest Articles in Lin. Alg. and Appl. during October-November 2013)

### Papers in Proceedings

1. Non-complex methods in the theory of real Banach algebras, Math. Student (India), 46 (1978), 49-53.
2. Numerical approximation of eigenvalues and eigenvectors, in Proceedings of the International Symposium on Modern Analysis and its Applications', held at I.I.T. Delhi in 1983, Prentice-Hall of India, New Delhi, 1986, 335-349.
3. Localization results for eigenelements, in Proceedings of the International Symposium on Modern Analysis and its Applications', held at I.I.T. Delhi in 1983, Prentice-Hall of India, New Delhi, 1986, 161-178 (with M.T. Nair).
4. Rayleigh-Schrodinger procedure for iterative refinement of computed eigenelements under strong approximation, in Proceedings of the International Conference on Methods of Functional Analysis in Approximation Theory', held at I.I.T. Bombay in 1985, Birkhauser Verlag, Basel, 1986, 371-388 (with M.T. Nair).
5. Spectral approximation, Math. Student (India), 65 (1996), 36-44.
6. The \ell_1 and \ell_infty solutions for an overdetermined system, Tubinger Berichte (Germany), 3 (1996), 211-226 (with A. Largillier).
7. Spectral approximation for compact integral operators, in Proceedings of the Seventh International Conference on Integral Methods in Science and Engineering: Analytic and Numerical Techniques', held at Universite Jean Monnet, St. Etienne (France) in 2002, Birkhauser, Boston, 2003, 115-122.
8. On acceleration of spectral computations for integral operators with weakly singular kernels, in Proceedings of the Ninth International Conference on Integral Methods in Science and Engineering: Techniques and Applications', held at Niagara Falls (Canada) in 2006, Birkhauser, Boston, 2007, 9-16 (with M. Ahues and A. Largillier).
9. Operator approximation, in Proceedings of the International Conference on Semigroups, Algebras and Operator Theory', held at Cochin University of Science and Technology, Kochi (India) in 2014, Springer Proceedings in Mathematics and Statistics, Vol 142, Springer India 2015, 135-147.