Random Blaschke products

Author:
W. George Cochran

Journal:
Trans. Amer. Math. Soc. **322** (1990), 731-755

MSC:
Primary 30D50; Secondary 30B20, 30C15, 30D55

DOI:
https://doi.org/10.1090/S0002-9947-1990-1022163-8

MathSciNet review:
1022163

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Abstract: Let be a sequence of independent random variables uniformly distributed on , and let for a fixed but arbitrary sequence of radii satisfying the Blaschke condition . We show that the random Blaschke product with zeros is almost surely not in the little Bloch space, and we describe necessary conditions and sufficient conditions on the radii so that is almost surely an interpolating sequence.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-1022163-8

Keywords:
Random,
Blaschke product,
Bloch space,
interpolating sequence,
interpolation

Article copyright:
© Copyright 1990
American Mathematical Society