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08 February 2025
 
  » arxiv » 1605.0359

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Duhamel convolution product in the setting of Quantum calculus
F. Bouzeffour ; M. T. Garayev ;
Date 2 May 2016
AbstractIn this paper we introduce the notions of $q$-Duhamel product and $q$-integration operator. We prove that the classical Wiener algebra $W(mathbb{D})$ of all analytic functions on the unit disc $mathbb{D}$ of the complex plane $mathbb{C}$ with absolutely convergent Taylor series is a Banach algebra with respect to $q$-Duhamel product. We also describe the cyclic vectors of the $q$-integration operator on $W(mathbb{D})$ and characterize its commutant in terms of the $q$-Duhamel product operators.
Source arXiv, 1605.0359
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