Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

Palle E.T Jorgensen; Steen Pedersen

doi:10.1063/1.1323499

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Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

Journal article

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Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

Palle E.T Jorgensen and Steen Pedersen

Journal of mathematical physics, Vol.41(12), pp.8263-8278

2000

DOI: 10.1063/1.1323499

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Abstract

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(∂/∂x j ):j=1,…,d} with domain C c ∞ (Ω) where the self-adjointness is defined relative to L 2 (Ω), and Ω is a given open subset of R d . The measure on Ω is Lebesgue measure on R d restricted to Ω. The problem originates with Segal and Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when Ω=I×Ω 2 and I is an open interval. We then apply the results to the case when Ω is a d cube, I d , and we describe possible subsets Λ⊂ R d such that {e λ | I d :λ∈Λ} is an orthonormal basis in L 2 (I d ).

Details

Title: Subtitle: Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
Creators: Palle E.T Jorgensen
Steen Pedersen
Resource Type: Journal article
Publication Details: Journal of mathematical physics, Vol.41(12), pp.8263-8278
DOI: 10.1063/1.1323499
ISSN: 0022-2488
eISSN: 1089-7658
Language: English
Date published: 2000
Academic Unit: Mathematics
Record Identifier: 9983985860902771

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