Multidimensional Euclidean Case
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Transmutation operators associated with Bessel functions expansions are defined. For these operators, the following basic questions are studied: the generalized homomorphism property with respect to suitable convolution algebras, support properties, the homeomorphism property with respect to suitable distribution spaces, explicit inversion formulas, the images of certain special functions, normative-type estimates, connections with the dual Abel transform, and applications to positive definite functions. The generalized homomorphism property is the crucial one; it relates the mean periodicity on multidimensional Euclidean spaces to that on ℝ1 and allows many proofs to be carried out by reduction to the one-dimensional case.
KeywordsEntire Function Spherical Function Inversion Formula Convolution Equation Nonempty Open Subset
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