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Bargmann measures for t-deformed probability

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Języki publikacji
EN
Abstrakty
EN
It is shown that the Bargmann representation of a t-deformed probability measure can be obtained by taking away some t-dependent amount of mass at zero of the Bargmann representation of the original measure and scaling of the remaining part. This allows us to formulate conditions on existence of the Bargmann representation of a t-deformed probability measure and to study some prominent examples.
Rocznik
Strony
279--291
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
  • Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] N. I Akhiezer, The Classical Moment Problem and some Related Questions in Analysis, Oliver and Boyd, Edinburgh and London 1965.
  • [2] N. Asai, I. Kubo, and H. H Kuo, Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures, Proc. Amer. Math. Soc. 131 (2) (2002), pp. 815-823.
  • [3] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform I, Comm. Pure Appl. Math. 14 (1961), pp. 187-214.
  • [4] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform II, Comm. Pure Appl. Math. 20 (1967), pp. 1-101.
  • [5] C. Berg, Recent results about moment problems, in: Probability Measures on Groups and Related Structures, XI Proceedings Oberwolfach 1994, H. Heyer (Ed.), World Scientific, Singapore 1995, pp. 1-13.
  • [6] C. Berg and M. Thill, Rotation invariant moment problem, Acta Math. 167 (3-4) (1991), pp. 207-227.
  • [7] M. Bożejko and J. Wysoczański, New examples of convolutions and non-commutative central limit theorems, Banach Center Publ. 43 (1998), pp. 95-103.
  • [8] M. Bożejko and J. Wysoczański, Remarks on t-transformations of measures and convolutions, Ann. Inst. H. Poincaré Probab. Statist. 37 (6) (2001), pp. 737-761.
  • [9] T. S. Chihara, An Introduction to Orthogonal Polynomials, Math. Appl., Vol. 13, Gordon and Breach, New York 1978.
  • [10] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York 1966.
  • [11] I. Królak, Measures connected with Bargmann’s representation of the q-commutation relations for q > 1, Banach Center Publ. 43 (1998), pp. 253-257.
  • [12] K. A. Penson and A. I. Solomon, New generalized coherent states, J. Math. Phys. 40 (5) (1999), pp. 2354-2363.
  • [13] J. A. Shohat and J. D. Tamarkin, The Problem of Moments, Math. Surveys No.1, American Mathematical Society, Providence 1943.
  • [14] B. Simon, The classical moment problem as a self-adjoint finite difference operator, Adv. Math. 137 (1998), pp. 82-203.
  • [15] J. Stochel and F. H. Szafraniec, The complex moment problem and subnormality: A polar decomposition approach, J. Funct. Anal. 159 (1998), pp. 432-491.
  • [16] F. H. Szafraniec, Operators of the q-oscillator, Banach Center Publ. 78 (2007), pp. 293-307.
  • [17] Ł. J. Wojakowski, Probability Interpolating between Free and Boolean, Dissertationes Math. 446 (2007).
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-251c89aa-c88b-40bd-b3e2-37a1c72b2953
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