A positivity result and normalization of positive convolution structures.
Michael Voit (1993)
Mathematische Annalen
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Michael Voit (1993)
Mathematische Annalen
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Dietmar Vogt, Reinhold Meise (1987/88)
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Tóth, László (1997)
Mathematica Pannonica
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T. Pytlik (1982)
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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...
S. R. Yadava (1972)
Matematički Vesnik
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J. Kucharczak (1988)
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Brian Fisher, Emin Özcag (1991)
Publications de l'Institut Mathématique
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J. Kucharczak (1973)
Colloquium Mathematicae
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Kazimierz Urbanik (1967)
Colloquium Mathematicum
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Speicher, Roland (1997)
Séminaire Lotharingien de Combinatoire [electronic only]
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S.P. AVANN (1964)
Mathematische Annalen
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B.R. SRINIVASAN (1965)
Mathematische Annalen
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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...
L.J. Mordell (1930)
Mathematische Annalen
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Kazimierz Urbanik (1987)
Colloquium Mathematicum
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