A q-analogue of convolution on the line

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dc.creatorCarnovale, G.
dc.creatorKoornwinder, T. H.
dc.date1999-09-03
dc.date2000-10-23
dc.date.accessioned2026-07-07T05:30:39Z
dc.date.available2026-07-07T05:30:39Z
dc.descriptionIn this paper we study a q-analogue of the convolution product on the line in detail. A convolution product on the braided line was defined algebraically by Kempf and Majid. We adapt their definition in order to give an analytic definition for the q-convolution and we study convergence extensively. Since the braided line is commutative as an algebra, all results can be viewed both as results in classical q-analysis and in braided algebra. We define various classes of functions on which the convolution is well-defined and we show that they are algebras under the defined product. One particularly nice family of algebras, a decreasing chain depending on a parameter running through (0,1], turns out to have 1/2 as the critical parameter value above which the algebras are commutative. Morerover, the commutative algebras in this family are precisely the algebras in which each function is determined by its q-moments. We also treat the relationship between q-convolution and q-Fourier transform. Finally, in the Appendix, we show an equivalence between the existence of an analytic continuation of a function defined on a q-lattice, and the behaviour of its q-derivatives.
dc.description31 pages; many small corrections; accepted by Methods and Applications of Analysis
dc.identifierhttps://arxiv.org/abs/math/9909025
dc.identifierhttp://arxiv.org/abs/math/9909025
dc.identifierMethods Appl. Anal. 7 (2000), 705-726
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79060
dc.subjectClassical Analysis and ODEs
dc.subjectQuantum Algebra
dc.subject33D80, 33D15, 42A85 (primary), 17B37 (secondary)
dc.titleA q-analogue of convolution on the line
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