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

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Abstract: We relate the decomposition over [*a*, *b*] of a measure (on ) into absolutely continuous, pure point, and singular continuous pieces to the behavior of integrals as . Here *F* is the Borel transform of , that is, .

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1277133-1

Article copyright:
© Copyright 1995
American Mathematical Society