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- W2091223759 abstract "The Lupaş q - transform emerges in the study of the limit q-Lupaş operator . The latter comes out naturally as a limit for a sequence of the Lupaş q -analogues of the Bernstein operator. Given q ∈ ( 0 , 1 ) , f ∈ C [ 0 , 1 ] , the q-Lupaş transform of f is defined by ( Λ q f ) ( z ) : = 1 ( − z ; q ) ∞ ⋅ ∑ 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, Λ q f is a meromorphic function whose poles are contained in the set J q : = { − q − j } j = 0 ∞ . In this paper, we study the connection between the behaviour of f on [ 0 , 1 ] and the decay of Λ q f as z → ∞ ." @default.
- W2091223759 created "2016-06-24" @default.
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- W2091223759 date "2012-10-01" @default.
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- W2091223759 title "Analytical properties of the Lupaş <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>q</mml:mi></mml:math>-transform" @default.
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- W2091223759 doi "https://doi.org/10.1016/j.jmaa.2012.04.047" @default.
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