Collection of Papers from the All-Union School on Function Theory

Collection of Papers from the All-Union School on Function Theory

by S. B. Stechkin
     
 

ISBN-10: 0821831364

ISBN-13: 9780821831366

Pub. Date: 12/31/1991

Publisher: American Mathematical Society

This collection consists of ten papers presented at the All-Union School on Function Theory, held in Dushanbe in August 1986, under the editor's guidance. The book encompasses a wide range of current directions in the metric theory of functions, the theory of approximation of functions, and related parts of mathematical analysis. The papers concern the following

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Overview

This collection consists of ten papers presented at the All-Union School on Function Theory, held in Dushanbe in August 1986, under the editor's guidance. The book encompasses a wide range of current directions in the metric theory of functions, the theory of approximation of functions, and related parts of mathematical analysis. The papers concern the following topics: extremal properties of functions, representation of functions by series, convergence of multiple Fourier series, approximation of functions by trigonometric polynomials in $L_p$-metrics, widths of classes of functions, approximation of functions by Fourier sums in systems of characters of zero-dimensional compact commutative groups, bilinear approximations of functions, the study of Tchebycheff sets in normed linear spaces, and spline approximation of functions of several variables. Among the results obtained are: new criteria for convexity of Tchebycheff sets in terms of continuity properties of the metric projection operator; conditions on the character of integrability of a periodic function of several variables under which its Fourier series converges to it in measure; a characterization of representation systems for symmetric spaces in which there are no nonzero continuous functionals.

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Product Details

ISBN-13:
9780821831366
Publisher:
American Mathematical Society
Publication date:
12/31/1991
Series:
Proceedings of the Steklov Institute of Mathematics Series, #189
Pages:
234

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