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In this paper, the generalized (two-parameterized) t-transformations on probability measures are introduced, in which the t-transformation of Bożejko and Wysoczański can be obtained as the special case, and the associated deformed convolutions are also investigated. We see that the generalized t-deformed free convolution can be realized as the conditionally free convolution of Bożejko, Leinert, and Speicher. We also study another special case of the generalized t-deformed free convolution, which is called the τ-free convolution, that gives an interpolation between the free and the Fermi convolutions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
97--119
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
autor
- Department of Information Sciences, Ochanomizu University, 2-1-1, Otsuka, Bunkyo, Tokyo, 112-8610 Japan
Bibliografia
- [1] N. I. Akhiezer, The Classical Moment Problem, Oliver and Boyd, Moscow 1961.
- [2] M. Bożejko, Deformed free probability of Voiculescu, RIMS Kokyuroku Kyoto Univ. 1227 (2001), pp. 96-113.
- [3] M. Bożejko, M. Leinert, and R. Speicher, Convolution and limit theorems for conditionally free random variables, Pacific J. Math. 175 (1996), pp. 357-388.
- [4] M. Bożejko and J. Wysoczański, New examples of convolution and non-commutative central limit theorems, Banach Center Publ. 43 (1998), pp. 95-103.
- [5] M. Bożejko and J. Wysoczański, Remarks on t-transformations of measures and convolutions, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), pp. 737-761.
- [6] J. M. Cohen and A. R. Trenholme, Orthogonal polynomials with constant recursion formula and an application to harmonic analysis, J. Funct. Anal. 59 (1984), pp. 175-184.
- [7] F. Oravecz, Fermi convolution, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), pp. 235-242.
- [8] 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), pp. 159-170.
- [9] R. Speicher, A new example of 'Independence' and 'White Noise’: Probab. Theory Related Fields 84 (1990), pp. 141-159.
- [10] H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, New York 1948.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ec6e85e4-c705-4a32-ba5b-6828e11b4455