Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup: Hermite property and its applications

Leiba Rodman; Ilya M. Spitkovsky

doi:10.1016/j.jfa.2008.05.010

Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup: Hermite property and its applications

Leiba Rodman, Ilya M. Spitkovsky

Mathematics

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

Abstract

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.

Original language	English (US)
Pages (from-to)	3188-3207
Number of pages	20
Journal	Journal of Functional Analysis
Volume	255
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2008.05.010
State	Published - Dec 1 2008

Keywords

Almost periodic functions
Factorization
Hermite rings
Matrix functions
Toeplitz corona
Wiener algebra

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2008.05.010

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title = "Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup: Hermite property and its applications",

abstract = "It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.",

keywords = "Almost periodic functions, Factorization, Hermite rings, Matrix functions, Toeplitz corona, Wiener algebra",

author = "Leiba Rodman and Spitkovsky, {Ilya M.}",

note = "Funding Information: The research of both authors was supported in part by NSF Grant DMS-0456625. Corresponding author. E-mail addresses: lxrodm@math.wm.edu (L. Rodman), ilya@math.wm.edu (I.M. Spitkovsky). URLs: http://www.math.wm.edu/~lxrodm (L. Rodman), http://www.math.wm.edu/~ilya (I.M. Spitkovsky).",

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doi = "10.1016/j.jfa.2008.05.010",

language = "English (US)",

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T1 - Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup

T2 - Hermite property and its applications

AU - Rodman, Leiba

AU - Spitkovsky, Ilya M.

N1 - Funding Information: The research of both authors was supported in part by NSF Grant DMS-0456625. Corresponding author. E-mail addresses: lxrodm@math.wm.edu (L. Rodman), ilya@math.wm.edu (I.M. Spitkovsky). URLs: http://www.math.wm.edu/~lxrodm (L. Rodman), http://www.math.wm.edu/~ilya (I.M. Spitkovsky).

PY - 2008/12/1

Y1 - 2008/12/1

N2 - It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.

AB - It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.

KW - Almost periodic functions

KW - Factorization

KW - Hermite rings

KW - Matrix functions

KW - Toeplitz corona

KW - Wiener algebra

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DO - 10.1016/j.jfa.2008.05.010

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SN - 0022-1236

VL - 255

SP - 3188

EP - 3207

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 11

ER -

Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup: Hermite property and its applications

Abstract

Keywords

ASJC Scopus subject areas

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