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Kolmogorov widths and approximation numbers of Sobolev classes with singular weights


Author: A. A. Vasil′eva
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 1.
Journal: St. Petersburg Math. J. 24 (2013), 1-27
MSC (2010): Primary 41A46
DOI: https://doi.org/10.1090/S1061-0022-2012-01229-X
Published electronically: November 15, 2012
MathSciNet review: 3013292
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Abstract: The Kolmogorov widths of weighted Sobolev classes in weighted $ L_q$-spaces and the approximation numbers of the corresponding embedding operators are estimated. The case where the weights affect the asymptotics is considered.


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Additional Information

A. A. Vasil′eva
Affiliation: Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia
Email: vasilyeva{\textunderscore}nastya@inbox.ru

DOI: https://doi.org/10.1090/S1061-0022-2012-01229-X
Keywords: Weighted Sobolev classes, Kolmogorov widths, approximation numbers
Received by editor(s): June 15, 2010
Published electronically: November 15, 2012
Additional Notes: Supported by RFBR (grants nos. 09-01-00093 and 10-01-00442)
Article copyright: © Copyright 2012 American Mathematical Society