A Hölder inequality for norms of Poissonian Wick products. (English) Zbl 1279.60087
Summary: An understanding of the second quantization operator of a constant times the identity operator and the Poissonian Wick product, without using the orthogonal Charlier polynomials, is presented first. We use both understanding, with and without the Charlier polynomials, to prove some inequalities about the norms of Poissonian Wick products. These inequalities are the best ones in the case of \(L^{1}\), \(L^{2}\), and \(L^{\infty}\) norms. We close the paper with some probabilistic interpretations of the Poissonian Wick product.
MSC:
60H40 | White noise theory |
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
46B70 | Interpolation between normed linear spaces |
Keywords:
Poissonian Wick product; second quantization operator; Hölder inequality; Stein analytic interpolation theorem; Poisson Wick exponential functions; {\(\alpha\)}-thinningReferences:
[1] | DOI: 10.1090/S0002-9939-02-06564-4 · Zbl 1028.46038 · doi:10.1090/S0002-9939-02-06564-4 |
[2] | DOI: 10.1142/S0219025711004456 · Zbl 1230.44002 · doi:10.1142/S0219025711004456 |
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[7] | DOI: 10.1090/S0002-9947-1956-0082586-0 · doi:10.1090/S0002-9947-1956-0082586-0 |
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