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Mat. Zametki, 2015, Volume 97, Issue 2, Pages 191–202 (Mi mz9371)  

An Analog of Wiener's Theorem for Infinite-Dimensional Banach Spaces

A. V. Zagorodnjuka, M. A. Mitrofanovb

a Vasyl Stefanyk Precarpathian National University
b Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine

Abstract: In this paper, we study various generalizations of the classical Wiener algebra on a Banach space and prove analogs of Wiener's theorem on the invertibility of elements of such algebras.

Keywords: Wiener algebra, Banach space, Wiener's theorem, Fourier series, convolution algebra, maximal ideal, Banach algebra, Aron–Berner extension.

Funding Agency Grant Number
State Fund for Fundamental Researches (Ukraine) Ф35/531-2011
This work was supported by the Ukrainian State Foundation for Basic Research (grant no. F35/531-2011).


DOI: https://doi.org/10.4213/mzm9371

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English version:
Mathematical Notes, 2015, 97:2, 179–189

Bibliographic databases:

UDC: 517
Received: 13.03.2012
Revised: 12.08.2014

Citation: A. V. Zagorodnjuk, M. A. Mitrofanov, “An Analog of Wiener's Theorem for Infinite-Dimensional Banach Spaces”, Mat. Zametki, 97:2 (2015), 191–202; Math. Notes, 97:2 (2015), 179–189

Citation in format AMSBIB
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