Collection Of Papers From The All Union School On Function Theory

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 polymonials in Lp-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.

Volume 190, issue 1 of 4. Translated from the Russian. Comprises materials of the All-Union School on the Theory of Functions (October 1987, Amberd), presenting papers on the coefficients of cosine series with nonnegative partial sums, bases in function spaces and the Franklin system, vectors with c

This volume contains papers presented at the All-Union School on the Theory of Functions, held in Miass in July 1989. The papers examine topical trends in the theory of functions and their approximation. Among the topics included are extremal properties of functions, approximation and interpolation of functions by trigonometric polynomials and splines, widths of function classes, best approximation of operators, cubature formulas, and classical problems of analytic number theory.