CaltechAUTHORS
  A Caltech Library Service

L^p Norms of the Borel Transform and the Decomposition of Measures

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

[img] PDF - Published Version
See Usage Policy.

278kB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20180206-140113065

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).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.2307/2161903DOIArticle
https://www.jstor.org/stable/2161903?seq=1#page_scan_tab_contentsJSTORArticle
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
NSFDMS-9101715
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

Repository Staff Only: item control page