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

Share this page *Edited by *
*S. B. Stechkin*

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.