Generalized free Gaussian white noise

  • Authors

    • Hakeem Othman Head of Department of Mathematics, University College of Al-Qunfudah,Umm Alqura Uniersity, Alkhalidya, Alqunfuhah city, Kingdom of Saudi
    2016-03-27
    https://doi.org/10.14419/ijams.v4i1.5911
  • Chebychev polynomials, Wigner semicircle distribution, Fourier transform, Wigner semicircle white noise
  • 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. [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.

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  • How to Cite

    Othman, H. (2016). Generalized free Gaussian white noise. International Journal of Advanced Mathematical Sciences, 4(1), 18-20. https://doi.org/10.14419/ijams.v4i1.5911