Multi-dimensional Poisson transform and applications
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Abstract
In this paper, we consider several new types of multi-dimensional Poisson transforms for the functions with values in complex Banach spaces.
We also prove some new properties of multidimensional vector-valued Laplace transform and analyze certain connections between the solutions of the abstract fractional partial differential equations and the abstract fractional partial difference equations.
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Keywords
Multi-dimensional Poisson transform, multi-dimensional fractional calculus, multidimensional vector-valued Laplace transform, abstract partial fractional differential-difference equations