Sequences, Summability and Fourier Analysis deals with various aspects of summability, a major branch of Analysis. The subject grew extensively during the twentieth century through the contribution of eminent analysts, but there are numerous unsolved problems, which still baffle the present-day scholars, as the application side has been poorly attended to. This volume contains original research articles, many valuable survey articles on approximation theory, multivalent functions, almost convergence and absolute almost convergence, Tauberian theorems, Kothe-Toeplitz duals of sequence spaces, random Fourier series, stochastic integrals, interpolative subspaces of Banach space, metric transformations in sequence spaces, absolute summability and Norlund summability.
D. Rath.: Kesharpur (New Colony), Cuttack - 753001, India S. Nanda.: Department of Mathematics Indian Institute of Technology Kharagpur, Kharagpur - 721302, India
Preface / On a Scale of Convergences / Absolute Riesz Summability of the type exp(wa) and its applications to Fourier Series / Degree of Approximation of Function of Bounded Variation by Cesaro Mean / Unconditional Convergence and Nuclear Spaces/ Closed convex Hull of Multivalent Symmetric Closed-to-Convex Functions of Order b / Some Generalized Difference Sequence Space and Their Koth - Toeplitz Duals / Absolute and Strong Almost Convergence (With Indices Defined by a Modulus) / Best Simultaneous Approximations and Simultaneous Farthest Points / Matrix Transformations on Sequence Spaces over Valued Fields / On Tauberian Theorem / Random Fourier Series, Stochastic Integrals and Applications / Interpolative Subspaces of a Banach Space / Matrix Transformations on Spaces of Almost Convergent Sequences and Those Defined by Full Classes of Natural Number Sets / Some Banach Algebras of Operator Matrices and Their Subalgebras / Statistical Convergence / On the Generalized Vector Sequence Space F (Î q, n) / Embedding Theorems in Functional Analysis / Tauberian Theorems Concerning the Summability Method of Logarithmic Type / On the Study of Maximal Groups in the Theory of Summability / Some Absolute Comparision Theorems on Product of (N, p, q) Methods