On a convolution type integral I
S. R. Yadava (1972)
Matematički Vesnik
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S. R. Yadava (1972)
Matematički Vesnik
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Brian Fisher, Emin Özcag (1991)
Publications de l'Institut Mathématique
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Mathematica Pannonica
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Anna Dorota Krystek (2010)
Banach Center Publications
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Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation of probability measures on the real line ℝ, which is another possible generalization of the t-transformation. Using that deformation we define a new convolution by deformation of the free convolution. The central limit measure with respect to the -deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the...
Nedeljkov, M., Pilipović, S. (1992)
Publications de l'Institut Mathématique. Nouvelle Série
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Kazimierz Urbanik (1987)
Colloquium Mathematicum
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Anna Kula (2011)
Banach Center Publications
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The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
J. Kucharczak (1988)
Colloquium Mathematicae
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E. Gesztelyi (1970)
Annales Polonici Mathematici
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Stojanović, Mirjana (1996)
Novi Sad Journal of Mathematics
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J. Kucharczak (1973)
Colloquium Mathematicae
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Kazimierz Urbanik (1967)
Colloquium Mathematicum
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Kislisçman, Adem (2003)
International Journal of Mathematics and Mathematical Sciences
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Brian Fisher (1991)
Annales Polonici Mathematici
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Kazimierz Urbanik (1987)
Colloquium Mathematicum
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Melanie Hinz, Wojciech Młotkowski (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.
Kilicman, Adem, Kamel Ariffin, Muhammad Rezal (2002)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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W. Okrasiński (1980)
Annales Polonici Mathematici
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