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Minakshisundaram, S.
- On the Structure of Unitary Symplectic Groups
Authors
1 Andhra University, Waltair, IN
Source
The Journal of the Indian Mathematical Society, Vol 19, No 3-4 (1955), Pagination: 105-120Abstract
In this note a few properties of the unitary symplectic group, USp(n), are studied. The results obtained seem to be interesting in themselves. Some of the properties of the unitary group of order 2 get themselves generalized easily.
- A Note on Typical Means
Authors
1 Tata Institute of Fundamental Research, Bombay, IN
2 Andhra University, Waltair, IN
Source
The Journal of the Indian Mathematical Society, Vol 18, No 1 (1954), Pagination: 107-114Abstract
This note has for its object the clarification of certain points in our book [1]. This clarification seems to us to be necessary in order to remove possible misconceptions regarding the validity of some of the results in [I] which are discussed in [2]; it will appear that those results are correct. We take this opportunity also to touch on some points other than those arising from [2], Chapter and page references, unless otherwise indioated, apply to the book.- Eigenfunctions on Riemannian Manifolds
Authors
1 Andhra University, Waltair, IN
Source
The Journal of the Indian Mathematical Society, Vol 17, No 4 (1953), Pagination: 159-165Abstract
In this note I give an alternative proof of some of the properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, which Pleijel and I proved some time back [2]. Instead of using Carleman's method, I use the heat equation as I did in the case of the Euclidean space [1].- On the Differentiated Series of Eigenfunctions
Authors
Source
The Journal of the Indian Mathematical Society, Vol 8 (1944), Pagination: 75-78Abstract
Let f(x,y) be a function integrable L2 in a bounded closed domain D whose boundary C is composed of a finite number of regular curves and let f(x,y)∼Σanωn(x,y), (i) where ωn(x,y) are the eigenfunctions.- On Expansion in Eigenfunctions of Boundary Value Problems IV
Authors
Source
The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 17-24Abstract
In III we studied the problem of summability of the Fourier series of an arbitrary function.- On Expansion in Eigenfungtions of Boundary Value Problems V
Authors
Source
The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 89-95Abstract
The present paper is concerned with the problem of absolute convergence of Fourier series of f(x, y) given by f(x,y)∼Σanωn(x,y) (1)
ωn(x,y) being the eigenfunctions of
Δω + μω = 0; ω(x,y) = 0 on C (2)
corresponding to the eigenvalues μn.
- Fourier Ansatz and Non-Linear Parabolic Equations
Authors
1 Andhra University, IN
Source
The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 129-142Abstract
Fourier Ansatz and Non-Linear Parabolic Equations.- Studies in Fourier Ansatz and Parabolic Equations
Authors
Source
The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 41-50Abstract
The crux of the method consists in reducing the above problem, to a problem in continuous transformation of an abstract space into itself and then applying Fixpunktsatz of Schauder.- On Expansion in Eigenfunctions of Boundary Value Problems III (The Summability Problem)
Authors
1 Madras, IN
Source
The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 153-167Abstract
The scope of this paper is to solve a problem raised by me in Paper I, of the same title.
Let D be a bounded open domain, simply or multiply connected, whose boundary C is composed of a finite number of regular curves in the (x,y) plane, and let wn(x,y) be the complete normal orthogonal eigenfunctions with the eigenvalues μn>0, n=1, 2,...of the boundary value problem.
- On the Expansion of an Arbitrary Function in a Series of Eigenfunctions of Boundary Value Problems II
Authors
1 Madras University, IN
Source
The Journal of the Indian Mathematical Society, Vol 5 (1941), Pagination: 103-108Abstract
Let D be a bounded open domain, simply or multiply connected, whose boundary C is composed of a finite number of regular curves in the x,y plane, and let wn(x,y) be the eigenfunctions (normal and orthogonal) with the corresponding eigenvalues λn > 0, n = 1, 2 , . . . of the boundary value problem.- On the Roots of a Continuous Non-Differentiable Function
Authors
Source
The Journal of the Indian Mathematical Society, Vol 4 (1940), Pagination: 31-33Abstract
Let f (x) be a continuous non-differentiable function defined in the interval (0,1), whose upper and lower bounds are l and u, say. If l ≤ α ≤ u, we denote by S(α), the set of points x in (0, 1) for which f(x)=α. It is known that S(α) is closed and non-dense. We now divide the interval (l, u) into three distinct sets of points A, B and C, so that A+B+C = (l, u), and
(a) A = the set of points a for which is of positive measure
(b) B = the set of points α for which S(α) is non-enumerable but of measure zero
(c) C = the set of points α for which S(α) is enumerable.
- A Tauberian Theorem on (λ, k)-Process of Summation
Authors
1 Madras University, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 127-130Abstract
I propose to prove here a generalization of a theorem due to Karamata on the (λ, k)-process of summation. This result includes all known Tauberian theorems on this process and can be applied to prove similar results on power series and Dirichlet's series.- On V. Ramaswami's Tauberian Theorem of Oscillation
Authors
1 Madras University, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 131-135Abstract
In this paper I give a simple and direct proof of Theorem A based on certain auxiliary theorems interesting in themselves. The method of proof closely resembles the one used by Szasz in some of his recent papers.- On the Theory of Non-Linear Partial Differential Equations of the Parabolic Type
Authors
1 Madras University, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 237-247Abstract
On the Theory of Non-Linear Partial Differential Equations of the Parabolic Type.- Tauberian Theorems on Dirichlet's Series
Authors
1 Madras, IN
Source
The Journal of the Indian Mathematical Society, Vol 2 (1937), Pagination: 147-155Abstract
The object of this paper is to prove that these theorems are true even when r > 1. The argument used is similar to that used in Theorem 22 of the Cambridge Tract on The General Theory of Dirichlet's Series by Hardy and Riesz. Some remarks are also made in the concluding section about the applications of these Tauberian theorems to obtain certain precise results on the abcissae of summability of Dirichlet's series. These results have been anticipated by Ananda Rau.- On the Extension of a Theorem of Caratheodory in the Theory of Fourier Series
Authors
1 Madras University, IN
Source
The Journal of the Indian Mathematical Society, Vol 2 (1937), Pagination: 314-320Abstract
The aim of this paper is to prove certain results which are converses of the following theorem in the theory of Fourier Series.
THEOREM A . Let {fk(x)}, 0≤x≤2π, k-1, 2.........
be a uniformly bounded sequence of measurable functions convergent almost everywhere to a measurable function F(x).
- The Fourier Series of a Sequence of Functions
Authors
1 Madras University, IN
Source
The Journal of the Indian Mathematical Society, Vol 2 (1937), Pagination: 321-323Abstract
Let fk(x)εLr, r≥1, in 0≤2π, k=1, 2... . Let an(k)→An, bn(k)→Bn, as k→∞ for each n. A necessary and sufficient condition that (An, Bn) should be the Fourier series of a function F(x)εLr which is the limit in the mean of {fk(x)} is that
lim lim x(k)n=0.