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Generalized Fock space . (English) Zbl 1240.30222

Usingf the generalized differentiation operator in the one-dimensional case, generalized Fock spaces are defined and their basic properties are studied. The operator conjugated to the operator of multiplication of independent variables is found and its eigenvalues and eigenfunctions are determined. A generalized Laplace transform is considered. Bases are constructed for the introduced spaces.

MSC:

30H20 Bergman spaces and Fock spaces
46B99 Normed linear spaces and Banach spaces; Banach lattices
46E99 Linear function spaces and their duals
44A10 Laplace transform
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