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arXiv · 2206.02726

On a Characterization of the Rellich-Kondrachov Theorem on Groups

Vernny Ccajma·Wladimir Neves·Jean Silva
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Abstract

Motivated by an eigenvalue-eigenfunction problem posed in IR^n x {\Omega}, where {\Omega} is a probability space, we are concerned in this paper with the Sobolev space on groups. Hence it is established an equivalence between locally compact Abelian groups and the space of solutions to the associated variational problem. Then, we study some conditions which characterize in a precisely manner the Rellich-Kondrachov Theorem, the principal ingredient to solve the variational problem.

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Vernny Ccajma, Wladimir Neves, Jean Silva. 2022-06-06. On a Characterization of the Rellich-Kondrachov Theorem on Groups. https://arxiv.org/abs/2206.02726

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