Multiplicative renormalization and generating functions I

Taiwanese Journal of Mathematics

Volumn 7, Issue 1, 2003, Pages 89-101

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

^a KYOTO UNIVERSITY   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

^c LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Fock space; Generating functions; Orthogonal polynomials; Segal Bargmann transforms; Szeg Jacobi parameters

Indexed keywords

EID: 16244404689     PISSN: 10275487     EISSN: None     Source Type: Journal    
DOI: 10.11650/twjm/1500407519     Document Type: Article

References (11)

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), pp. 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. Kubo and H.-H. Kuo, Multiplicative renormalization and generating functions II; (under preparation).
6. T. S. Chihara, An Introduction to Orthogonal Polynomials. Gordon and Breach, 1978.
7. A. Erdélyi, (editor): Higher Transcendental Functions III, Bateman Manuscript Project. McGraw Hill, 1955.
8. T. Hida, Analysis of Brownian Functionals. Carleton Mathematical Lecture Notes 13, 1975.
9. S. Hitotsumatsu, S. Moriguchi and K. Udagawa, Mathematical Formulas III, Special Functions. Iwanami, 1975.
10. H.-H. Kuo, White Noise Distribution Theory. CRC Press, 1996.
11. M. Szegö, Orthogonal Polynomials. Coll. Publ. 23, Amer. Math. Soc., 1975.