On the Lupas <i>q</I>-transform
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Date
2011
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Publisher
Pergamon-elsevier Science Ltd
Open Access Color
HYBRID
Green Open Access
No
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Abstract
The Lupas q-transform emerges in the study of the limit q-Lupas operator. The latter comes out naturally as a limit for a sequence of the Lupas q-analogues of the Bernstein operator. Lately, it has been studied by several authors from different perspectives in mathematical analysis and approximation theory. This operator is closely related to the q-deformed Poisson probability distribution, which is used widely in the q-boson operator calculus. (Lambda(q)f)(z) := 1/(-z; q)(infinity) . Sigma(infinity)(k=0) f(1 - q(k))q(k(k-1)/2)/(q; q)(k) z(k). In this paper, we study some analytic properties of (Lambda(q)f)(z). In particular, we examine the conditions under which Lambda(q)f can either be an entire function, or a rational one. (C) 2010 Elsevier Ltd. All rights reserved.
Description
Keywords
q-integers, q-binomial theorem, Lupas q-analogue of the Bernstein operator, Analytic function, Meromorphic function, q-integers, Analytic function, q-binomial theorem, Meromorphic function, Lupaş q-analogue of the Bernstein operator, Lupaş \(q\)-analogue of the Bernstein operator, \(q\)-integers, Approximation by operators (in particular, by integral operators), analytic function, \(q\)-binomial theorem, Miscellaneous topics of analysis in the complex plane, meromorphic function, Special integral transforms (Legendre, Hilbert, etc.)
Fields of Science
0101 mathematics, 01 natural sciences
Citation
WoS Q
Q1
Scopus Q
OpenCitations Citation Count
6
Source
Computers & Mathematics with Applications
Volume
61
Issue
3
Start Page
527
End Page
532
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CrossRef : 5
Scopus : 8
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