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Bounds for entropy numbers for some critical operators


Author: M. A. Lifshits
Journal: Trans. Amer. Math. Soc. 364 (2012), 1797-1813
MSC (2010): Primary 47B06
DOI: https://doi.org/10.1090/S0002-9947-2011-05407-3
Published electronically: December 2, 2011
MathSciNet review: 2869192
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Abstract: We provide upper bounds for entropy numbers for two types of operators: summation operators on binary trees and integral operators of Volterra type. Our efforts are concentrated on the critical cases where none of the known methods work. Therefore, we develop a method which seems to be completely new and probably merits further applications.


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Additional Information

M. A. Lifshits
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
Email: lifts@mail.rcom.ru

DOI: https://doi.org/10.1090/S0002-9947-2011-05407-3
Keywords: Entropy numbers, integral operators, operators on trees
Received by editor(s): April 20, 2010
Published electronically: December 2, 2011
Additional Notes: This work was supported by RFBR-DFG grant 09-01-91331 and by RFBR grant 09-01-12180-ofi_m.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.