Multiplicative renormalization and generating functions II

Taiwanese Journal of Mathematics

Volumn 8, Issue 4, 2004, Pages 593-628

  Asai, Nobuhiro ^a   Kubo, Izumi ^b,c   Kuo, Hui Hsiung ^d  

^a KYOTO UNIVERSITY   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

^c HIROSHIMA INSTITUTE OF TECHNOLOGY   (Japan)

^d LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Generating function; Interacting Fock space; Multiplicative renormalization; Orthogonal polynomials; Pre generating function; Szeg Jacobi parameters

Indexed keywords

EID: 7444251626     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500407706     Document Type: Article

References (13)

1. L. Accardi and M. Bożejko, Interacting Fock space and Gaussianization of probability measures; Infinite Dimensional Analysis, Quantum Probability and Related Topics. 1 (1998), 663-670.
2. N. Asai, Analytic characterization of one-mode interacting Fock space; Infinite Dimensional Analysis, Quantum Probability and Related Topics. 4 (2001) 409-415.
3. N. Asai, Integral transform and Segal-Bargmann representation associated to q-Charlier polynomials; in Quantum Information IV, T. Hida and K. Saitô (eds.), World Scientific, 2002, 39-48.
4. 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 (2003), 815-823. (Article electronically published on July 2, 2002).
5. N. Asai, I, Kub and H.-H. Kuo, Multiplicative renormalization and generating functions I; Taiwanese Journal of Mathematics 7 (2003), 89-101.
6. N. Asai, I. Kubo and H.-H. Kuo, Generating functions of orthogonal polynomials and Szegö-Jacobi parameters; Probability and Mathematical Statistics, 23 Fasc 2, (2003), 273-291.
7. T. S. Chihara, An Introduction to Orthogonal Polynomials. Gordon and Breach, 1978.
8. A. Erdélyi, (editor): Higher Transcendental Functions III, Bateman Manuscript Project. McGraw Hill, 1955.
9. T. Hida, Stationary Stochastic Processes. Princeton University Press, 1970.
10. T. Hida, Analysis of Brownian Functional. Carleton Mathematical Lecture Notes 13, 1975.
11. S. Hitotsumatsu, S. Moriguchi and K. Udagawa, Mathematical Formulas III, Special Functions. Iwanami, 1975.
12. H.-H. Kuo, White Noise Distribution Theory. CRC Press, 1996.
13. M. Szegö, Orthogonal Polynomials. Coll. Publ. 23, Amer. Math. Soc. 1975.