Frostman shifts of inner functions

Raymond Mortini; Artur Nicolau

doi:10.1007/BF02787765

Frostman shifts of inner functions

Raymond Mortini, Artur Nicolau

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

13 Citations (Scopus)

Abstract

In this paper we study the class M of all inner functions whose non-zero Frostman shifts are Carleson-Newman Blaschke products. We present several geometric, measure theoretic and analytic characterizations of M in terms of level sets, distribution of zeros, and behaviour of pseudohyperbolic derivatives and observe that M is the set of all functions in H∞ whose range on the set of trivial points in the maximal ideal space is ∂double struck D sign ∪ {0}.

Original language	English
Pages (from-to)	285-326
Journal	Journal d'Analyse Mathematique
Volume	92
DOIs	https://doi.org/10.1007/BF02787765
Publication status	Published - 1 Jan 2004

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AB - In this paper we study the class M of all inner functions whose non-zero Frostman shifts are Carleson-Newman Blaschke products. We present several geometric, measure theoretic and analytic characterizations of M in terms of level sets, distribution of zeros, and behaviour of pseudohyperbolic derivatives and observe that M is the set of all functions in H∞ whose range on the set of trivial points in the maximal ideal space is ∂double struck D sign ∪ {0}.

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