Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition. (English) Zbl 1050.60070
Summary: Duality is established for new spaces of entire functions in two infinite-dimensional variables with certain growth rates determined by Young functions. These entire functions characterize the symbols of generalized Fock space operators. As an application, a proper space is found for a solution to a normal-ordered white noise differential equation having highly singular coefficients.
MSC:
60H40 | White noise theory |
46E50 | Spaces of differentiable or holomorphic functions on infinite-dimensional spaces |
47N30 | Applications of operator theory in probability theory and statistics |
Keywords:
Fock space; operator symbol; infinite-dimensional holomorphy; normal-ordered white noise differential equation; quantum white noiseReferences:
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