Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Random Blaschke products


Author: W. George Cochran
Journal: Trans. Amer. Math. Soc. 322 (1990), 731-755
MSC: Primary 30D50; Secondary 30B20, 30C15, 30D55
MathSciNet review: 1022163
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \{ {\theta _n}(\omega )\} $ be a sequence of independent random variables uniformly distributed on $ [0,2\pi ]$, and let $ {z_n}(\omega ) = {r_n}{e^{i{\theta _n}(\omega )}}$ for a fixed but arbitrary sequence of radii $ {r_n}$ satisfying the Blaschke condition $ \sum {(1 - {r_n}) < \infty } $. We show that the random Blaschke product with zeros $ {z_n}(\omega )$ is almost surely not in the little Bloch space, and we describe necessary conditions and sufficient conditions on the radii $ {r_n}$ so that $ \{ {z_n}(\omega )\} $ is almost surely an interpolating sequence.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30D50, 30B20, 30C15, 30D55

Retrieve articles in all journals with MSC: 30D50, 30B20, 30C15, 30D55


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-1022163-8
PII: S 0002-9947(1990)1022163-8
Keywords: Random, Blaschke product, Bloch space, interpolating sequence, interpolation
Article copyright: © Copyright 1990 American Mathematical Society