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Dilations and Mehler's kernel

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Abstract

An explicit formula for the second quantization of a contraction matrix on a finite dimensional Hilbert space is derived by means of dilation theory. When the dimension is one, this reduces to Mehler's formula.

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References

  1. Kuo, H.H.: Gaussian Measures in Banach Spaces. Lecture Notes in Mathematics, v. 463. New York, Springer-Verlag 1975.

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  3. Simon, B.: The P(φ)2 Euclidean (Quantum) Field Theory. Princeton, N.J., Princeton University Press 1974.

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  4. Sz.-Nagy, B. and Foias, C: Harmonic Analysis of Operators on Hilbert Space. North Holland Amsterdam 1970.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, 22903, Charlottesville, Virginia, USA

    James S. Howland

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  1. James S. Howland
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Supported by NSF Grant MCS-74-07313-A03

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Howland, J.S. Dilations and Mehler's kernel. Integr equ oper theory 2, 130–137 (1979). https://doi.org/10.1007/BF01729365

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  • DOI: https://doi.org/10.1007/BF01729365

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