Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ L\sp p$ norms of the Borel transform and the decomposition of measures


Author: B. Simon
Journal: Proc. Amer. Math. Soc. 123 (1995), 3749-3755
MSC: Primary 44A15; Secondary 28A10
MathSciNet review: 1277133
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We relate the decomposition over [a, b] of a measure $ d\mu $ (on $ \mathbb{R}$) into absolutely continuous, pure point, and singular continuous pieces to the behavior of integrals $ \smallint\limits_a^b {{(\operatorname{Im} F(x + i\epsilon ))}^p}dx$ as $ \epsilon \downarrow 0$. Here F is the Borel transform of $ d\mu $, that is, $ F(z) = \smallint {(x - z)^{ - 1}}d\mu (x)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 44A15, 28A10

Retrieve articles in all journals with MSC: 44A15, 28A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1277133-1
PII: S 0002-9939(1995)1277133-1
Article copyright: © Copyright 1995 American Mathematical Society