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- W1967449403 abstract "For each τ0>0 we denote by S(τ0) = {z∈C:|Imz|<τ0} the strip parallel to the real axes. Further by H(τ0) and Ĥ(τ0) we denote the Frèshet spaces of all analytic functions, defined in S(τ0) and having representation there in series of Hermite polynomials, respectively in series of Hermite functions. Also, by Δ(λ0), λ0>0 we denote the interior of parabola p(λ0rpar; with focus at the origin and vertex at the point −λ02, and by L(λ0)—the Frèshet space of all analytic functions, defined in Δ(λ0) and having representations in series of Laguerre polynomials {Ln(α)(z)}n = 0∞, α∈C (we mean here only the values of parameter α, for which the sets of functions, having representation in series of Laguerre polynomials with parameter α coincide).We prove that the spaces H(τ0) and Ĥ(τ0) are isomorphic, also that the space L(λ0) is isomorphic to the closed subspace He(λ0)⊂H(τ0) of all even functions." @default.
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- W1967449403 date "2010-01-01" @default.
- W1967449403 modified "2023-09-23" @default.
- W1967449403 title "Isomorphisms between some special spaces of analytic functions" @default.
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- W1967449403 doi "https://doi.org/10.1063/1.3515579" @default.
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