Interpolations of Bargmann type measures

• Autorzy: Asai N. , Krystek A. D. , Wojakowski Ł. J.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we shall discuss Bargmann type measures on C for several classes of probability measures on R. The unified interpolation expressions include not only the classical Bargmann measure and its q-deformation, but also their t-deformations and dilations. As a special case, we get conditions on existence and an explicit form of the Bargmann representation for the free Meixner family of probability measures.

Słowa kluczowe

EN

Bargmann representation; deformation; complex moment problem

PL

reprezentacja Bargmanna; deformacja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 3
• Strony: 293--301
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Asai N.

• Department of Mathematics, Aichi University of Education Kariya, 448-8542, Japan

autor

Krystek A. D.

• Mathematical Institute, University of Wrocław Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Wojakowski Ł. J.

• Mathematical Institute, University of Wrocław Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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• [10] A. Hora, N. Obata, Quantum Probability and Spectral Analysis of Graphs, Springer, 2007.
• [11] A. D. Krystek, Ł. J. Wojakowski, Bargmann measures for t-deformed probability, Probab. Math. Statist. 34(2) (2014), 279–291.
• [12] H. van Leeuwen, H. Maassen, A q deformation of the Gauss distribution, J. Math. Phys. 36 (1995), 4743–4756.
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• [15] Ł. J. Wojakowski, Probability interpolating between free and boolean, Dissertationes Math. 446(45) (2007), 45pp.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.