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A general approach to approximation problems of the Bernstein type

Authors
Journal
Advances in Mathematics
0001-8708
Publisher
Elsevier
Publication Date
Volume
49
Issue
3
Identifiers
DOI: 10.1016/0001-8708(83)90063-4
Disciplines
  • Mathematics

Abstract

Abstract The Bernstein approximation problem is treated in a general setting of Banach function spaces. An abstract theory is developed which includes as special cases the solutions of the Bernstein problem given by Mergelyan and Pollard. It also provides a unified setting for related results from polynomial and trigonometric approximation theory and yields as corollaries a number of new results.

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