Published December 1995
| Published
Journal Article
Open
L^p Norms of the Borel Transform and the Decomposition of Measures
- Creators
-
Simon, B.
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).
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.Attached Files
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Additional details
- Eprint ID
- 84693
- Resolver ID
- CaltechAUTHORS:20180206-140113065
- DMS-9101715
- NSF
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2018-02-06Created from EPrint's datestamp field
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2021-11-15Created from EPrint's last_modified field