Spectral theory of commuting self-adjoint partial differential operators

DOI10.1016/0022-1236(87)90061-9zbMath0651.47038OpenAlexW1968190356MaRDI QIDQ1106453

Steen Pedersen

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0022-1236(87)90061-9

zbMATH Keywords

Fourier transformLie groupspectral setlocally compact abelian groupdual groupspectral pairintegrability propertyregular positive Borel measurestrongly continuous unitary representation

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of partial differential operators (47F05) Spectral sets of linear operators (47A25) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (28)

Harmonic analysis on tori ⋮ Duality questions for operators, spectrum and measures ⋮ Spectral sets and factorizations of finite abelian groups ⋮ Fourier analysis on domains in compact groups ⋮ Wavelets associated with nonuniform multiresolution analyses and one-dimensional spectral pairs ⋮ Hadamard triples generate self-affine spectral measures ⋮ Harmonic analysis of fractal measures ⋮ Nonuniform wavelets and wavelet sets related to one-dimensional spectral pairs ⋮ Spectrum is periodic for \(n\)-intervals ⋮ Fourier frequencies in affine iterated function systems ⋮ Momentum operators in the unit square ⋮ Early influences, the Fuglede question, spectrum vs tiling, and connection to related work by John von Neumann, Irving Segal, Marshall Stone, and David Shale ⋮ Spectrality of self-similar tiles ⋮ Frames of exponentials and sub-multitiles in LCA groups ⋮ Positive definite functions on the Heisenberg group ⋮ Fuglede’s conjecture for a union of two intervals ⋮ Hilbert spaces of distributions having an orthogonal basis of exponentials ⋮ Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives ⋮ Lattice sub-tilings and frames in LCA groups ⋮ Orthogonal harmonic analysis of fractal measures ⋮ Duality properties between spectra and tilings ⋮ Fuglede's conjecture fails in 4 dimensions over odd prime fields ⋮ Nonuniform multiresolution analyses and spectral pairs ⋮ Dense analytic subspaces in fractal \(L^2\)-spaces ⋮ Orthonormal bases of exponentials for the \(n\)-cube ⋮ Spectral theory of multiple intervals ⋮ Spectral pairs in Cartesian coordinates ⋮ Translation representations and scattering by two intervals

Cites Work

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• On Fourier transforms of functions supported on sets of finite Lebesgue measure
• Partial differential operators and discrete subgroups of a Lie group
• Spectral theory of finite volume domains in \(R^ n\).
• On groups of automorphisms of operator algebras
• Commuting self-adjoint partial differential operators and a group theoretic problem
• On rings of operators. Reduction theory
• The projection spectral theorem
• Cardinality of discrete subsets of a topological space

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