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Fourier transform of a Gaussian measure on the Heisenberg group. (English) Zbl 1102.60003

Summary: An explicit formula is derived for the Fourier transform of a Gaussian measure on the Heisenberg group at the Schrödinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two Gaussian measures to be a Gaussian measure.

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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