On the Lupas <i>q</i>-transform
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Date
2011
Authors
Ostrovska, Sofiya
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Publisher
Pergamon-elsevier Science Ltd
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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.
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Keywords
q-integers, q-binomial theorem, Lupas q-analogue of the Bernstein operator, Analytic function, Meromorphic function
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Citation
8
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Q1
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Volume
61
Issue
3
Start Page
527
End Page
532