Widths and optimal quadrature formulas for convolution classes

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1991 English Publisher:Springer Science and Business Media LLCJournal:Ukrainian Mathematical Journal, volume 43, pages 1,064-1,076 (issn: 0041-5995, eissn: 1573-9376,

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Authors: V. F. Babenko;

doi: 10.1007/bf01089204

Widths and optimal quadrature formulas for convolution classes

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Abstract

We compute Kolmogorov widths in the space L1 for classes of periodic functions representable in the form of a kernel convolution that does not increase the number of sign changes with values in a given transposition invariant set of functions, and solve the optimization problem for quadrature formulas in these classes.

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