Variations around a general quantum operator
type: Item
instance of: scholarly article
title: Variations around a general quantum operator
zbMATH Open document ID: 1476.33015
published in: The Ramanujan Journal
publication date: 2021-05-06T00:00:00Z
review text: The authors take the quantum operator \[ D_{\beta}[f](t):=\frac{f(\beta(t))-f(t)}{\beta(t)-t} \] with suitable function \(\beta\), and study the basic properties of this operator, and also of its operator inverse, from function space viewpoint. They define the function space \[ \mathscr{L}_{\beta}^{p}[a, b]=\left\{f:\left.I \rightarrow \mathbb{C}\left|\int_{a}^{b}\right| f\right|^{p} \mathrm{~d}_{\beta}<\infty\right\}. \] It turns out that this space is a Banach space. Among other things, Hölder's inequality is also proven.
Mathematics Subject Classification ID: 33E20
Mathematics Subject Classification ID: 33E30
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 40A10
zbMATH DE Number: 7344944
zbMATH Keywords: general quantum difference operator
zbMATH Keywords: \(\beta\)-derivative
zbMATH Keywords: \(\beta\)-integral
zbMATH Keywords: \(\beta\)-Lebesgue spaces
zbMATH Keywords: \(q\)-analogues
zbMATH Keywords: Jackson \(q\)-integral
author: J. L. Cardoso
reviewed by: István Mező
MaRDI profile type: Publication
full work available at URL: s11139-019-00210-8
OpenAlex ID: W3006588880
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DOI: 10.1007/S11139-019-00210-8
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description: scientific article; zbMATH DE number 7344944