Simon, B. (1995) L^p Norms of the Borel Transform and the Decomposition of Measures. Proceedings of the American Mathematical Society, 123 (12). pp. 3749-3755. ISSN 0002-9939. doi:10.2307/2161903. https://resolver.caltech.edu/CaltechAUTHORS:20180206-140113065
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Abstract
We relate the decomposition over [a, b] of a measure dµ (on R) into absolutely continuous, pure point, and singular continuous pieces to the behavior of integrals _α∫^b(ImF(x + iε))^P dx as ε ↓ 0. Here F is the Borel a transform of dµ, that is, F(z) = (x - z)^(-1) dµ(x).
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| Additional Information: | © 1995 American Mathematical Society. Received by the editors March 25, 1994 and, in revised form, May 23, 1994. This material is based upon work supported by National Science Foundation Grant No. DMS-9101715. It is a pleasure to thank S. Jitomirskaya, A. Klein, and T. Wolff for valuable discussions. | |||||||||
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| Issue or Number: | 12 | |||||||||
| Classification Code: | 1991 Mathematics Subject Classification. Primary 28B99 | |||||||||
| DOI: | 10.2307/2161903 | |||||||||
| Record Number: | CaltechAUTHORS:20180206-140113065 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180206-140113065 | |||||||||
| Official Citation: | L^p Norms of the Borel Transform and the Decomposition of Measures B. Simon Proceedings of the American Mathematical Society Vol. 123, No. 12 (Dec., 1995), pp. 3749-3755 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 84693 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 06 Feb 2018 22:27 | |||||||||
| Last Modified: | 15 Nov 2021 20:22 |
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