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Quantum compound Poisson processes and white noise analysis

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Differential and Integral Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 102))

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Abstract

We consider a family B of self-adjoint commuting operators b ς = ∫ ς(t) dB t where B t is a quantum compound Poisson process in a Fock space. By using the projection spectral theorem, we construct the Fourier transform in generalized joint eigenvectors of the family B which is unitary between the Fock space and the L 2-space of compound Poisson white noise, (L 2CP). This construction gives the possibility of introducing spaces of test and generalized functions the dual pairing of which is determined by the inner product of (L 2 CP)

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Author information

Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska St., 252601, Kiev, Ukraine

    E. W. Lytvynov

Authors
  1. E. W. Lytvynov
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Editors and Affiliations

  1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  2. NWFI-Mathematik, Universität Regensburg, D-93040, Regensburg, Germany

    R. Mennicken  & C. Tretter  & 

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© 1998 Springer Basel AG

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Lytvynov, E.W. (1998). Quantum compound Poisson processes and white noise analysis. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Differential and Integral Operators. Operator Theory: Advances and Applications, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8789-2_11

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  • DOI: https://doi.org/10.1007/978-3-0348-8789-2_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9774-7

  • Online ISBN: 978-3-0348-8789-2

  • eBook Packages: Springer Book Archive

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