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Collection of Papers from the All-Union School of Function Theory
Edited by: S. B. Stechkin
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Proceedings of the Steklov Institute of Mathematics
1991; 234 pp; softcover
Volume: 189
ISBN-10: 0-8218-3136-4
ISBN-13: 978-0-8218-3136-6
List Price: US$135 Member Price: US$108
Order Code: STEKLO/189

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.