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

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dc.creatorJorgensen, Palle E. T.
dc.creatorPedersen, Steen
dc.date2000-05-24
dc.date.accessioned2026-07-07T04:35:31Z
dc.date.available2026-07-07T04:35:31Z
dc.descriptionWe consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(Ω) where the self-adjointness is defined relative to L^2(Ω), and Ωis a given open subset of R^d. The measure on Ωis Lebesgue measure on R^d restricted to Ω. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when Ω=I\timesΩ_2 and I is an open interval. We then apply the results to the case when Ωis a d-cube, I^d, and we describe possible subsets Λof R^d such that {e^(i2πλ\dot x) restricted to I^d:λ\inΛ} is an orthonormal basis in L^2(I^d).
dc.descriptionLaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km, 02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt, 61.44.Br
dc.identifierhttps://arxiv.org/abs/math/0005248
dc.identifierhttp://arxiv.org/abs/math/0005248
dc.identifierJ. Math. Phys. 41 (2000), 8263--8278
dc.identifierdoi:10.1063/1.1323499
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59279
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject42C05, 22D25, 46L55, 47C05
dc.titleCommuting self-adjoint extensions of symmetric operators defined from the partial derivatives
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