Published December 1995 | Version Published
Journal Article Open

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

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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).

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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84693
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CaltechAUTHORS:20180206-140113065

Funding

NSF
DMS-9101715

Dates

Created
2018-02-06
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Updated
2021-11-15
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