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Abstrakty
The Nevalinna transform (…) of a positive measure (…) and a constant a, plays an important role in complex analysis and - more recently - in the context of the boolean convolution. We show here that its restriction to the imaginary axis, (…), can be expressed as the Laplace transform of the Fourier transform (a characteristic function) of (…). Consequently, (…) is sufficient for the unique identification of the measure (…) and the constant a. Finally, we identify a relation between the free additive Voiculescu (…) and boolean convolutions.
Wydawca
Czasopismo
Rocznik
Tom
Strony
297--307
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
autor
- Institute Of Mathematics University of Wroclaw Pl. Grunwaldzki 2/4 50-384 Wroclaw, Poland, zjjurek@math.uni.wroc.pl
Bibliografia
- [1] N. I. Akhiezer, The Classical Moment Problem, Oliver & Boyd, Edinburgh and London, 1965.
- [2] H. Bercovici, D. Voiculescu, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42(3) (1993), 733–773.
- [3] Ph. Biane, Processes with free increments, Math. Z. 227 (1998), 143–174.
- [4] L. Bondesson, Generalized Gamma Convolutions and Related Classes of Distributions and Densities, Springer-Verlag, New York, 1992.
- [5] G. P. Chistyakov, F. Götze, The arithmetic of distributions in free probability theory, 2005. arXiv:math.OA/0508245
- [6] I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, San Diego; 5th Edition, 1994.
- [7] Z. J. Jurek, Cauchy transforms of measures viewed as some functionals of Fourier transforms, Probab. Math. Statist. 26(1) (2006), 187–200.
- [8] Z. J. Jurek, Random integral representations for free-infinitely divisible and tempered stable distributions, Statist. Probab. Lett. 77 (2007), 417–425.
- [9] S. Lang, SL2 ( R ), Addison-Wesley, Reading Massachusetts, 1975.
- [10] R. Lenczewski, Decompositions of the free additive convolution, J. Funct. Anal. 246 (2007), 330–365.
- [11] R. Speicher, R. Woroudi. Boolean convolution, Fields Inst. Commun. 12 (1997), 267–279.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0034-0028