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A generalization to locally compact abelian groups of a spectral problem for commuting partial differential operators
Journal article   Open access   Peer reviewed

A generalization to locally compact abelian groups of a spectral problem for commuting partial differential operators

Journal of pure and applied algebra, Vol.25(3), pp.297-301
1982
DOI: 10.1016/0022-4049(82)90084-6
url
https://doi.org/10.1016/0022-4049(82)90084-6View
Published (Version of record) Open Access

Abstract

Let G be a locally compact abelian group, and let Ω be an open relatively compact subset of positive Haar measure. Let Λ be a subset of the dual group G such that the restriction to Ω of Λ(·) for λϵΛ constitute an orthonormal basis for L 2 (Ω) with normalized measure. We show that the pair Ω,Λ can be characterized completely in terms of group theory and the geometry of fundamental domains for discrete subgroups. Proofs are only sketched. The relationship to partial differential operators is pointed out.

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