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Institution Author: Ostrovska, Sofiya (35610828900)Subject: Analytic function

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Now showing 1 - 3 of 3
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    Article
    The Inversion Results for the Limit q-bernstein Operator
    (Springer Basel Ag, 2018) Ostrovska, Sofiya
    The limit q-Bernstein operator B-q appears as a limit for a sequence of the q-Bernstein or for a sequence of the q-Meyer-Konig and Zeller operators in the case 0 < q < 1. Lately, various features of this operator have been investigated from several angles. It has been proved that the smoothness of f is an element of C[0, 1] affects the possibility for an analytic continuation of its image B-q f. This work aims to investigate the reciprocal: to what extent the smoothness of f can be retrieved from the analytical properties of B-q f.
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    Citation - WoS: 8
    Citation - Scopus: 8
    On the Lupas q-transform
    (Pergamon-elsevier Science Ltd, 2011) Ostrovska, Sofiya
    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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    Citation - WoS: 5
    Citation - Scopus: 5
    Analytical Properties of the Lupas q-transform
    (Academic Press inc Elsevier Science, 2012) Ostrovska, Sofiya
    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. Given q is an element of (0, 1), f is an element of C left perpendicular0, 1right perpendicular, the q-Lupas transform off is defined by (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). The transform is closely related to both the q-deformed Poisson probability distribution, which is used widely in the q-boson operator calculus, and to Valiron's method of summation for divergent series. In general, Lambda(q)f is a meromorphic function whose poles are contained in the set J(q) := {-q(-j)}(j=0)(infinity). In this paper, we study the connection between the behaviour of f on leftperpendicular0, 1right perpendicular and the decay of Lambda(q)f as z -> infinity. (C) 2012 Elsevier Inc. All rights reserved.