Duhamel convolution product in the setting of Quantum calculus

2016/05/02 by F. Bouzeffour, Bouzeffour, F., M. T. Garayev +1
Mathematics · #33D45 #96J15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33D45 #msc:96J15

paper · pdf · doi:10.48550/arxiv.1605.00359

9

arxiv created 2016/05/02 · arxiv updated 2016/05/03

Abstract

In this paper we introduce the notions of q-Duhamel product and q-integration operator. We prove that the classical Wiener algebra W(\mathbbD) of all analytic functions on the unit disc \mathbbD of the complex plane 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(\mathbbD) and characterize its commutant in terms of the q-Duhamel product operators.

Related

• A q-analogue of convolution on the line
• D-polynomials and Taylor formula in quantum calculus
• On the Quantum Quarter Plane and the Real Quantum Plane
• Rational Hadamard products via Quantum Diagonal Operators
• Some Banach algebra structures for l^p(β) and their operators