Titlebook: Analytic Extension Formulas and their Applications; Saburou Saitoh,Nakao Hayashi,Masahiro Yamamoto Book 2001 Springer Science+Business Med

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https://doi.org/10.1007/978-1-4899-2040-9 and the Calogero model. To this end we regard the solution .(., ·) as an analytic function of time . and construct both a generalized Fourier cosine transform and a generalized Fourier sine transform. Moreover, we show an embedding theorem of Sobolev type as another application of these transforms.

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,A Sampling Principle Associated with Saitoh’s Fundamental Theory of Linear Transformations,sociated with this series expansion is discussed..The sampling principle of Kramer is generalized in this context, and several examples are given where the kernels arise from polynomials of Meixner type.

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Holomorphic Spaces Related to Orthogonal Polynomials and Analytic Continuation of Functions,to be extended are assumed in the hypotheses. Incidentally, new orthogonality properties of the Hermite and Laguerre polynomials and necessary and sufficient conditions for square summability with geometric weight .. of the coefficients in these polynomials are proved.

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Analytic Extension Formulas and their Applications

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