A fundamental approach to the generalized eigenvalue problem for self- adjoint operators

DOI10.1016/0022-1236(85)90098-9zbMath0587.47026OpenAlexW2134533626MaRDI QIDQ1072085

S. J. L. van Eijndhoven, J. de Graaf

Publication date: 1985

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(85)90098-9

zbMATH Keywords

Gelfand tripleeigenfunctions which are tempered distributionsgeneralized eigenvalue problem for an arbitrary self-adjoint operatormeasure theoretical version of the Sobolev lemmamultiplicity theory for self-adjoint operators

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Operations with distributions and generalized functions (46F10) Linear symmetric and selfadjoint operators (unbounded) (47B25) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (6)

Positive sesquilinear form measures and generalized eigenvalue expansions ⋮ Recovering a large number of diffusion constants in a parabolic equation from energy measurements ⋮ Recovering time-dependent diffusion coefficients in a nonautonomous parabolic equation from energy measurements ⋮ Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra ⋮ Modules, completely positive maps, and a generalized KSGNS construction ⋮ Maximality of positive operator-valued measures

Cites Work

• A measure theoretical Sobolev lemma
• A mathematical interpretation of Dirac's formalism; Part B: Generalized eigenfunctions in trajectory spaces
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