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Article overview
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Duhamel convolution product in the setting of Quantum calculus | F. Bouzeffour
; M. T. Garayev
; | Date: |
2 May 2016 | Abstract: | In 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 | Services: | Forum | Review | PDF | Favorites |
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