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Proceedings of an All-Union School on the Theory of Functions (Miass, July 1989)
Edited by: S. B. Stechkin
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Proceedings of the Steklov Institute of Mathematics
1994; 255 pp; softcover
Volume: 198
ISBN-10: 0-8218-3153-4
ISBN-13: 978-0-8218-3153-3
List Price: US$198
Member Price: US$158.40
Order Code: STEKLO/198
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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.

Readership

Research mathematicians.

Table of Contents

  • V. V. Arestov -- Best approximation of translation invariant unbounded operators by bounded linear operators
  • M.-B. A. Babaev -- On the order of approximation of the Sobolev class \(W_q^r\) by bilinear forms in \(L_p\) for \(1\le q\le 2\le p\le \infty\)
  • V. M. Badkov -- Asymptotic and extremal properties of orthogonal polynomials in the presence of singularities in the weight
  • Yu. S. Vasil'ev -- Approximation by splines on an infinite interval
  • S. V. Konyagin -- On estimates of Gaussian sums and Waring's problem for a prime modulus
  • O. V. Matveev -- Spline interpolation of functions of several variables, and bases in Sobolev spaces
  • A. V. Reztsov -- On errors of parallelepiped cubature formulas on classes of differentiable functions
  • V. V. Tarkaev -- On divergence of Fourier series in rearranged Price systems
  • D. S. Telyakovskiĭ -- On asymptotically monogenic functions
  • S. A. Telyakovskiĭ -- On approximation of differentiable functions of high smoothness by Fourier sums
  • N. N. Kholshchevnikova -- On some thin sets in the theory of functions and topology
  • I. G. Tsar'kov -- Widths and an inequality of Jackson type for abstract functions
  • N. I. Chernykh -- Jackson's inequality in \(L_p(0,2\pi )\) \((1\le p< 2)\) with sharp constant
  • V. T. Shevaldin -- Lower estimates of the widths of some classes of periodic functions
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