Commuting self-adjoint partial differential operators and a group theoretic problem
From MaRDI portal
Publication:1843037
DOI10.1016/0022-1236(74)90072-XzbMath0279.47014MaRDI QIDQ1843037
Publication date: 1974
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Groups and semigroups of linear operators (47D03) General theory of partial differential operators (47F05)
Related Items
Orthogonal Exponentials of Planar Self-Affine Measures with Four-Element Digit Set, Spectrality of a class of Moran measures on with consecutive digit sets, Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$, On Riesz Bases of Exponentials for Convex Polytopes with Symmetric Faces, Packing near the tiling density and exponential bases for product domains, Harmonic analysis of fractal measures induced by representations of a certain 𝐶*-algebra, Hadamard triples generate self-affine spectral measures, On the structure of spectral and tiling subsets of cyclic groups, SPECTRALITY AND NON-SPECTRALITY OF PLANAR SELF-SIMILAR MEASURES WITH FOUR-ELEMENT DIGIT SETS, SPECTRUM OF A SELF-AFFINE MEASURE WITH FOUR-ELEMENT DIGIT SET, The Fuglede Conjecture Holds in, Parseval frames from compressions of Cuntz algebras, The cardinality of orthogonal exponentials of planar self-affine measures with two-element digit set, The spectrality of symmetric additive measures, On \(p\)-adic spectral measures, A NONSPECTRAL PROBLEM FOR PLANAR MORAN–SIERPINSKI MEASURES, Some results on planar self-affine measures with collinear digit sets, Riesz bases of exponentials for multi-tiling measures, Spectral sets and weak tiling, Early influences, the Fuglede question, spectrum vs tiling, and connection to related work by John von Neumann, Irving Segal, Marshall Stone, and David Shale, Product-form Hadamard triples and its spectral self-similar measures, There are four-element orthogonal exponentials of planar self-affine measures with two digits, Tiling and spectrality for generalized Sierpinski self-affine sets, On the Fourier orthonormal bases of a class of self-similar measures on \(\mathbb{R}^n\), The spectral eigenmatrix problems of planar self-affine measures with four digits, The exact number of orthogonal exponentials of a class of Moran measures on \(\mathbb{R}^3\), Positive Weight Function and Classification of g-Frames, Non-spectrality of a class of Moran measures on \(\mathbb{R}^3\), Spectral properties of a class of Moran measures on \(\mathbb{R}^2\), Self-similar measures with product-form digit sets and their spectra, The spectra of Cantor-type measures with consecutive digits, Spectrality of a Class of Moran Measures, Spectral eigenmatrix of the planar spectral measures with four elements, The spectrality of a class of fractal measures on \(\mathbb{R}^n \), A set with no Riesz basis of exponentials, NON-SPECTRALITY OF THE PLANAR SELF-AFFINE MEASURES WITH FOUR-ELEMENT DIGIT SETS, Fourier bases of a class of planar self-affine measures, On the spectra of a class of Moran measures, Spectrality of Cantor-Moran measures with three-element digit sets, Spectral self-similar measures with alternate contraction ratios and consecutive digits, On rationality of spectrums for spectral sets in \(\mathbb{R} \), On self-affine tiles that are homeomorphic to a ball, ORTHOGONAL EXPONENTIAL FUNCTIONS OF THE PLANAR SELF-AFFINE MEASURES WITH FOUR DIGITS, Spectrality of Moran measures with finite arithmetic digit sets, Riesz bases of exponentials on unbounded multi-tiles, Reconstruction of Signals: Uniqueness and Stable Sampling, Fourier Bases and Fourier Frames on Self-Affine Measures, Some Recent Developments of Self-Affine Tiles, Spectra for cubes in products of finite cyclic groups, Multiple Spectra of Bernoulli Convolutions, Unnamed Item, THE NON-SPECTRAL PROPERTY OF A CLASS OF PLANAR SELF-SIMILAR MEASURES, Orthogonal exponentials of self-affine measures on ℝn, Spectral property of self-affine measures on \(\mathbb{R}^n\), Characterization of a class of planar self-affine tile digit sets, Duality relation on spectra of self-affine measures, Some approximation properties of hexagonal Fourier series, Unnamed Item, NUMBER THEORY PROBLEMS RELATED TO THE SPECTRUM OF CANTOR-TYPE MEASURES WITH CONSECUTIVE DIGITS, Fourier frames for singular measures and pure type phenomena, On the spectrality of self-affine measures with four digits on ℝ2, Spectrality of a class of self-affine measures on R2 *, Spectral property of self-affine measures on \(\mathbb{R}^n\), Some reductions of the spectral set conjecture to integers, On approximation of hexagonal Fourier series in the generalized Hölder metric, Orthogonal harmonic analysis of fractal measures, Orthogonal exponentials on the ball, On a problem of Turán about positive definite functions, Discrete Fourier analysis on a dodecahedron and a tetrahedron, On spectral sets of integers, Non-symmetric convex polytopes and Gabor orthonormal bases, ORTHOGONAL EXPONENTIAL FUNCTIONS OF SELF-AFFINE MEASURES IN ℝn, THE CARDINALITY OF ORTHOGONAL EXPONENTIAL FUNCTIONS ON THE SPATIAL SIERPINSKI GASKET, SPECTRAL PROPERTY OF CERTAIN MORAN MEASURES WITH THREE-ELEMENT DIGIT SETS, Degree of approximation by means of hexagonal Fourier series, Equi‐distributed property and spectral set conjecture on Zp2×Zp, Combinatorial and harmonic-analytic methods for integer tilings, Tiles with no spectra, Extensions of Laba-Wang's condition for spectral pairs, Unitary representations of wavelet groups and encoding of iterated function systems in solenoids, Crystallographic Groups, Strictly Tessellating Polytopes, and Analytic Eigenfunctions, Multiple lattice tiles and Riesz bases of exponentials, Spectral theory of multiple intervals, Trigonometric moment problems for arbitrary finite subsets of $\mathbb Z^n$, Gabor orthogonal bases and convexity, On Gabor orthonormal bases over finite prime fields, Spectra of measures and wandering vectors, A Weyl type formula for Fourier spectra and frames, Iterated function systems, Ruelle operators, and invariant projective measures, Approximation by means of hexagonal Fourier series in Hölder norms, Three Problems on Exponential Bases, Riesz bases of exponentials and the Bohr topology, Fuglede’s conjecture holds on ℤ_{𝕡}²×ℤ_{𝕢}, On spectral structure and spectral eigenvalue problems for a class of self similar spectral measure with product form, Spectrality of Moran Sierpinski-type measures on, INFINITE ORTHOGONAL EXPONENTIALS OF A CLASS OF SELF-AFFINE MEASURES, SPECTRAL EIGENVALUE PROBLEMS OF SELF-SIMILAR MEASURES WITH CONSECUTIVE DIGITS, Orthogonality relations on certain homogeneous spaces, Spectral Moran measures on R2 *, The cardinality of \(\mu_{M,D}\)-orthogonal exponentials for the planar four digits, On spectral and non-spectral problem for the planar self-similar measures with four element digit sets, Spectral sets and tiles in \(\mathbb{Z}_p^2 \times \mathbb{Z}_q^2\), Spectral structure of planar self-similar measures with four-element digit set, Fuglede's spectral set conjecture for convex polytopes, Spectrality of infinite convolutions with three-element digit sets, Resonances for open quantum maps and a fractal uncertainty principle, Fourier orthonormal bases of two dimensional Moran measures with four-element digits, Necessary conditions for interpolation by multivariate polynomials, Spectrality of self-affine measures on the three-dimensional Sierpinski gasket, Riesz bases of exponentials for convex polytopes with symmetric faces, On characterizations of Fourier frames and tilings, Convergence of mock Fourier series on generalized Bernoulli convolutions, \(L^p\)-\(L^q\) boundedness of Fourier multipliers on fundamental domains of lattices in \(\mathbb{R}^d\), An Operator-Fractal, Spectrality and non-spectrality of some Moran measures in \(\mathbb{R}^3\), Spectral property of certain Moran measures in \(\mathbb{R}^n\), On the Fourier orthonormal bases of a class of Moran measures on \(\mathbb{R}^2\), Tiling sets and spectral sets over finite fields, On exponential bases and frames with non-linear phase functions and some applications, Spaces invariant under unitary representations of discrete groups, Finding duality for Riesz bases of exponentials on multi-tiles, Spectrality of self-affine Sierpinski-type measures on \(\mathbb{R}^2\), Scaling of spectra of a class of random convolution on \(\mathbb{R}\), Spectrality of self-similar measures with product-form digits, On the discrete Fuglede and Pompeiu problems, Spectral property of certain fractal measures, Spectrality of product domains and Fuglede's conjecture for convex polytopes, Spectral property of the planar self-affine measures with three-element digit sets, Spectral properties of certain Moran measures with consecutive and collinear digit sets, Weak convergence and spectrality of infinite convolutions, The cardinality of orthogonal exponentials of planar self-affine measures with three-element digit sets, Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets, On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem, A characterization on the spectra of self-affine measures, The structure of multiplicative tilings of the real line, Spectrality of homogeneous Moran measures on \(\mathbb{R}^n\), Spectrality of Moran-Sierpinski type measures, On the spectra of a class of self-affine measures on \(\mathbb{R}^2\), Non-spectral problem for the planar self-affine measures with decomposable digit sets, A geometric construction of tight multivariate Gabor frames with compactly supported smooth windows, The Coven-Meyerowitz tiling conditions for 3 odd prime factors, Arbitrarily sparse spectra for self-affine spectral measures, Approximation properties of hexagonal Fourier series in the generalized Hölder metric, An extension of Łaba-Wang's theorem, Momentum operators in two intervals: spectra and phase transition, On self-similar spectral measures, Multi-tiling and Riesz bases, On spectral eigenvalue problem of a class of self-similar spectral measures with consecutive digits, On spectral \({N}\)-Bernoulli measures, 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, Spectrality of generalized Sierpinski-type self-affine measures, Spectrality of Moran-type self-similar measures on \(\mathbb{R} \), Frame spectral pairs and exponential bases, Inequalities for nonuniform wavelet frames, A class of homogeneous Moran spectral measures with eight-element digit sets on \(\mathbb{R}^4\), Tight wavelet frame sets in finite vector spaces, A pair of commuting hypergeometric operators on the complex plane and bispectrality, A counterexample to Fuglede's conjecture in \((\mathbb{Z}/p\mathbb{Z})^4\) for all odd primes, Fourier series and approximation on hexagonal and triangular domains, Spectral properties of some unions of linear spaces, Tiling functions and Gabor orthonormal basis, Fuglede's conjecture fails in 4 dimensions over odd prime fields, $(p, q)$-frame measures on LCA groups: perturbations and construction, Spectral Measures on Local Fields, Bounded tiles in \(\mathbb{Q}_p\) are compact open sets, Combining Riesz bases, Spectrality of Sierpinski-Moran measures, Spectrality of a class of infinite convolutions, Multiple spectra of self-similar measures with three digits on \(\mathbb{R}\), Spectrality of a class of self-affine measures and related digit sets, Spectrality of certain self-affine measures on the generalized spatial Sierpinski gasket, Tiling $$\mathbb{Z}^{2}$$ by a Set of Four Elements, Existence and exactness of exponential Riesz sequences and frames for fractal measures, Spectrality of a class of Moran measures, Scaling of spectra of random convolutions with three-element digit sets, On the orthogonal exponential functions of a class of planar self-affine measures, Spectrality of Sierpinski-type self-affine measures, Arithmetic sets in groups, Riesz wavelets, tiling and spectral sets in LCA groups, Fourier duality for fractal measures with affine scales, Spectral measures and Cuntz algebras, Structured Hadamard Conjecture, Non-spectrality of self-affine measures, Fuglede's conjecture holds in \(\mathbb{Q}_p\), On spectral eigenvalue problem of a class of generalized Cantor measures, Number theoretic related to the scaling spectrum of self-similar measure with three element digit sets, Fuglede's conjecture holds for cyclic groups of order \(pqrs\), Construction of a class of spectral measures, Non-separable lattices, Gabor orthonormal bases and tilings, Translation representations and scattering by two intervals, On the quasi-Beurling dimensions of the spectra for planar Moran-type Sierpinski spectral measures, Spectral property of a class of Moran measures on \(\mathbb{R}\), Tiling properties of spectra of measures, Non-spectrality of Moran measures with four digits, Sierpinski-type spectral self-similar measures, Gabor orthonormal bases generated by the unit cubes, Spectrality of infinite Bernoulli convolutions, The spectrality of self-affine measure under the similar transformation of \(GL_n(p)\), Fourier bases of the planar self‐affine measures with three digits, On the intermediate value property of spectra for a class of Moran spectral measures, Taking music seriously: on the dynamics of `mathemusical' research with a focus on hexachordal theorems, Fuglede’s Conjecture Holds in \(\boldsymbol{\mathbb{Z}_{p}\times \mathbb{Z}_{p^{n}}}\), On zeros and spectral property of self-affine measures, Spectral number of 3-Bernoulli convolutions on R and Sierpinski-type measures on R2, Spectrality of random convolutions generated by finitely many Hadamard triples, Infinite orthogonal exponentials for a class of Moran measures, Unnamed Item, Some properties of spectral measures, Spectral sets and tiles on vector space over local fields, On the spectra of Sierpinski-type self-affine measures, A counterexample to Dutkay-Jorgensen conjecture, On characterizations of spectra and tilings, Harmonic analysis on tori, Three-way tiling sets in two dimensions, Duality questions for operators, spectrum and measures, Spectral sets and factorizations of finite abelian groups, Spectrality and tiling by cylindric domains, Fourier analysis on domains in compact groups, Compact open spectral sets in \(\mathbb{Q}_p\), Wavelets associated with nonuniform multiresolution analyses and one-dimensional spectral pairs, Spectral theory of commuting self-adjoint partial differential operators, Spectra of Bernoulli convolutions and random convolutions, Spectra of Cantor measures, On a criterion of universal spectra, Harmonic analysis of fractal measures, Nonuniform wavelets and wavelet sets related to one-dimensional spectral pairs, Spectral self-affine measures on the planar Sierpinski family, \(\mu _{m,d}\)-orthogonality and compatible pair, Approximation on the Voronoi cells of the \(A_d\) lattice, Spectral property of Cantor measures with consecutive digits, Spectrum is periodic for \(n\)-intervals, Analysis of orthogonality and of orbits in affine iterated function systems, Fourier frequencies in affine iterated function systems, Spectrality of self-affine measures and generalized compatible pairs, Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups, Momentum operators in the unit square, Scaling of spectra of self-similar measures with consecutive digits, Spectrality of certain Moran measures with three-element digit sets, Partial differential operators and discrete subgroups of a Lie group, Spectrality of self-similar tiles, Distance sets relating to orthogonal exponentials, Spectral self-affine measures with prime determinant, Periodicity of the spectrum of a finite union of intervals, Spectra of a class of self-affine measures, Spectrality of planar self-affine measures with two-element digit set, The spin Sutherland model of \(D_N\) type and its associated spin chain, Frames of exponentials and sub-multitiles in LCA groups, Spectrality of Moran measures with four-element digit sets, Translational absolute continuity and Fourier frames on a sum of singular measures, Size of orthogonal sets of exponentials for the disk, Positive definite functions on the Heisenberg group, Spectra of certain types of polynomials and tiling of integers with translates of finite sets., On Fourier frame of absolutely continuous measures, Discrete Fourier analysis with lattices on planar domains, Spectral theory of finite volume domains in \(R^ n\)., When does a Bernoulli convolution admit a spectrum?, Extension of positive definite functions, Extensions of positive definite integral kernels on the Heisenberg group, A generalization to locally compact Abelian groups of a spectral problem for commuting partial differential operators, A class of spectral Moran measures, Exponential bases, Paley-Wiener spaces and applications, Analysis of a class of spectral pair conditions, On the universal tiling conjecture in dimension one, Spectral measures associated with the factorization of the Lebesgue measure on a set via convolution, Spectral properties of self-similar measures with product-form digit sets, On the rationality of the spectrum, Scaling functions on the spectrum, Spectrality of the planar Sierpinski family, Non-spectrality of self-affine measures on the spatial Sierpinski gasket, Spectrality of a class of Cantor-Moran measures, Approximation of continuous functions by matrix means of hexagonal Fourier series, Spectral measures generated by arbitrary and random convolutions, On the Fourier orthonormal bases of Cantor-Moran measures, Lattice sub-tilings and frames in LCA groups, Orthogonal exponentials on the generalized three-dimensional Sierpinski gasket, Combining Riesz bases in \(\mathbb{R}^d\), Orthogonal exponentials on the generalized plane Sierpinski gasket, Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure, The Fuglede conjecture holds in \(\mathbb{Z}_p\times \mathbb{Z}_p\), Non-spectral problem for a class of planar self-affine measures, Non-spectral problem for the planar self-affine measures, Turán's extremal problem on locally compact abelian groups, Discrete Fourier analysis on fundamental domain and simplex of \(A_{d}\) lattice in \(d\)-variables, Non-spectral self-affine measure problem on the plane domain, The structure of cube tilings under symmetry conditions, On the \(\mu_{M,D}\)-orthogonal exponentials, Nonuniform sampling and recovery of multidimensional bandlimited functions by Gaussian radial-basis functions, Families of spectral sets for Bernoulli convolutions, Duality properties between spectra and tilings, Selfadjoint extension operators commuting with an algebra, Orthogonal exponentials, translations, and Bohr completions, Spectral properties of a class of Moran measures, Quasiperiodic spectra and orthogonality for iterated function system measures, Spectral properties of small Hadamard matrices, On the spectra of momentum operators, Analysis of \(\mu_{R,D}\)-orthogonality in affine iterated function systems, Density results for Gabor systems associated with periodic subsets of the real line, Nonuniform multiresolution analyses and spectral pairs, Dense analytic subspaces in fractal \(L^2\)-spaces, Non-spectrality of planar self-affine measures with three-elements digit set, Orthonormal bases of exponentials for the \(n\)-cube, The cardinality of certain \(\mu _{M,D}\)-orthogonal exponentials, Distance sets that are a shift of the integers and Fourier basis for planar convex sets, Wavelets, tiling, and spectral sets, Spectral pairs in Cartesian coordinates, On spectral Cantor measures, Mock Fourier series and transforms associated with certain Cantor measures
Cites Work
