Limit measures related to the conditionally free convolution

• Autorzy: Hinz M. , Młotkowski W.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Cauchy transform; conditionally free product; Jacobi parameters

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 1
• Strony: 75--81
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Hinz M.

autor

Młotkowski W.

• Institut für Mathematik und Informatik, Ernst-Moritz-Arndt Universität Greifswald, Jahnstrasse 15a D-17487 Greifswald, Germany,

Bibliografia

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• [4] T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach.
• [5] M. Hinz and W. Młotkowski, Free cumulants of some probability measures, in: Banach Center Publ. 78, Inst. Math., Polish Acad. Sci., 2007, 165-170.
• [6] A. D. Krystek and L. J. Wojakowski, Associative convolutions arising from conditionally free convolution, Infin. Dim. Anal. Quantum Probab. Related Topics 8 (2005), 515-545.
• [7] N. Saitoh and H. Yoshida, The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory, Probab. Math. Statist. 21 (2001), 159-170.
• [8] D. Voiculescu, Symmetries of some reduced free product C*-algebras, in: Operator Algebras and their Connection with Topology and Ergodic Theory (Buşteni, 1983), Lecture Notes in Math. 1132, Springer, Heidelberg, 1985, 556-588.
• [9] D. Voiculescu, K. J. Dykema and A. Nica, Free Random Variables, CRM Monogr. Ser. 1, Amer. Math. Soc., 1992.