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Nonlinear Gaussian transformation in Hilbert spaces. (English) Zbl 1099.46053

This paper deals with a nonlinear generalization of the Gaussian integral transformation on separable real Hilbert space. In the present study, the authors describe a system where the random objects are measurable mappings taking values in a real separable Hilbert space. The sequence of corresponding measures can be studied by means of their Laplace transforms, which in certain cases may be extended to holomorphic functions. The mapping generating the sequences of such functions may be defined as a nonlinear integral transformation, a generalization of the Gaussian transformation \((S\)-transformation), which is an important element of the white noise analysis. A number of properties of the fixed points of the latter are obtained and the stability of these points is studied.

MSC:

46T25 Holomorphic maps in nonlinear functional analysis
60H40 White noise theory
46G20 Infinite-dimensional holomorphy
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References:

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