Inner Functions and Zero Sets for ℓpA

Authors

Raymond Cheng
Javad Mashreghi
William T. Ross, University of RichmondFollow

DOI

10.1090/tran/7675

Abstract

In this paper we characterize the zero sets of functions from l ^P_A (the analytic functions on the open unit disk D whose Taylor coefficients form an l ^P sequence) by developing a concept of an "inner function" modeled by Beurling's discussion of the Hilbert space l ² _A, the classical Hardy space. The zero set criterion is used to construct families of zero sets which are not covered by classical results. In particular, we give an alternative proof of a result of Vinogradov [Dokl. Akad. Nauk SSSR 160 (1965), pp. 263-266] which says that when p > 2, there are zero sets for l ^P _A which are not Blaschke sequences.

Document Type

Article

Publication Date

8-1-2019

Publisher Statement

Copyright © 2019, American Mathematical Society.

DOI: https://doi.org/10.1090/tran/7675.

Recommended Citation

Cheng, Raymond, Javad Mashreghi, and William T. Ross. “Inner Functions and Zero Sets for ℓpA .” Transactions of the American Mathematical Society 372, no. 3 (August 1, 2019): 2045–72. https://doi.org/10.1090/tran/7675.