Bounds for entropy numbers for some critical operators
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- by M. A. Lifshits
- Trans. Amer. Math. Soc. 364 (2012), 1797-1813
- DOI: https://doi.org/10.1090/S0002-9947-2011-05407-3
- Published electronically: December 2, 2011
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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.References
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Bibliographic Information
- M. A. Lifshits
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
- Email: lifts@mail.rcom.ru
- 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.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 1797-1813
- MSC (2010): Primary 47B06
- DOI: https://doi.org/10.1090/S0002-9947-2011-05407-3
- MathSciNet review: 2869192