Generalized free Gaussian white noise
DOI:
https://doi.org/10.14419/ijams.v4i1.5911Keywords:
Chebychev polynomials, Wigner semicircle distribution, Fourier transform, Wigner semicircle white noiseAbstract
Based on an adequate new Gel'fand triple, we construct the infinite dimensional free Gaussian white noise measure \(\mu\) using the Bochner-Minlos theorem. Next, we give the chaos decomposition of an \(L^{2}\) space with respect to the measure \(\mu\).
References
[1] N. Asai, I. Kubo and H.-H. Kuo, Multiplication Renormalization and Generating Function I., Taiwanese Journal of Mathematics, Vol. 8, No. 4 (2004), 583-628.
[2] T.S. Chihara, â€An introduction to Orthogonal Polynomialization†,Gordon and Breach, New York, 1978.
[3] G. Gasper and M. Rahman, †Basic hypergeometric seriesâ€, Vol 35 of Encyclopedia Of Mathematics And Its Application, Cambridge Universty Press, Cambridge (1990).
[4] Yu. G. Kondratiev, J.L. Silva, L. Streit and G.F. Us, â€Analysis on Pois-son and Gamma spaceâ€, Infinite dimensional anal. Quant. Probab, Vol. 1 No. 1 (1998), 91-118.
[5] H. Van Leeuwen and H. Maassen, â€A q-deformation of the Gauss distributionâ€, Journal of mathematical physic, 36(9), 4743-4756 [1995].
[6] H. Rguigui, â€Quantum l -potentials associated to quantum Ornstein-Uhlenbeck semigroupsâ€, Chaos, Solitons & Fractals, Volume 73, April 2015, Pages 80-89.