On the cyclic behavior of singular inner functions in Besov and sequence spaces

Alberto Dayan; Daniel Seco Fornsnacke

doi:10.1007/s43037-025-00467-w

On the cyclic behavior of singular inner functions in Besov and sequence spaces

Alberto Dayan, Daniel Seco Fornsnacke

Department of Mathematics

Facultad de Ciencias de la Información. Universidad de La Laguna. Revista Latina de Comunicación Social

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

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Abstract

We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure. Such singular inner functions are cyclic also in the space ℓAp of holomorphic functions with coefficients in ℓp. This can only happen for measures that place no mass on any Beurling-Carleson set.

Original language	English
Article number	2
Number of pages	19
Journal	Banach Journal of Mathematical Analysis
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s43037-025-00467-w
Publication status	Published - 30 Oct 2025

Keywords

Singular inner function
Sequence spaces
Cyclic vectors
30J15
30H99
47A16

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10.1007/s43037-025-00467-w

https://ddd.uab.cat/record/323062

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abstract = "We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure. Such singular inner functions are cyclic also in the space ℓAp of holomorphic functions with coefficients in ℓp. This can only happen for measures that place no mass on any Beurling-Carleson set.",

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AU - Seco Fornsnacke, Daniel

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Y1 - 2025/10/30

N2 - We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure. Such singular inner functions are cyclic also in the space ℓAp of holomorphic functions with coefficients in ℓp. This can only happen for measures that place no mass on any Beurling-Carleson set.

AB - We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure. Such singular inner functions are cyclic also in the space ℓAp of holomorphic functions with coefficients in ℓp. This can only happen for measures that place no mass on any Beurling-Carleson set.

KW - Singular inner function

KW - Sequence spaces

KW - Cyclic vectors

KW - 30J15

KW - 30H99

KW - 47A16

U2 - 10.1007/s43037-025-00467-w

DO - 10.1007/s43037-025-00467-w

M3 - Article

SN - 2662-2033

VL - 20

JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

IS - 1

M1 - 2

ER -

On the cyclic behavior of singular inner functions in Besov and sequence spaces

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Keywords

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