Spectral pairs in Cartesian coordinates

DOI10.1007/BF01259371zbMath1050.42016arXivmath/9912131OpenAlexW2026409692MaRDI QIDQ1302336

Palle E. T. Jorgensen, Steen Pedersen

Publication date: 1999

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9912131

zbMATH Keywords

Hilbert spacetilingsorthogonal basistranslationsinduced representationsoperator extensionsspectral resolutionFourier basisspectral pair

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Noncommutative dynamical systems (46L55) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Linear operators in algebras (47C05)

Related Items (52)

Spectral sets and tiles on vector space over local fields ⋮ Fuglede's spectral set conjecture for convex polytopes ⋮ On characterizations of spectra and tilings ⋮ On characterizations of Fourier frames and tilings ⋮ Duality questions for operators, spectrum and measures ⋮ Spectrality and tiling by cylindric domains ⋮ Compact open spectral sets in \(\mathbb{Q}_p\) ⋮ Hadamard triples generate self-affine spectral measures ⋮ SPECTRALITY AND NON-SPECTRALITY OF PLANAR SELF-SIMILAR MEASURES WITH FOUR-ELEMENT DIGIT SETS ⋮ Spectrality of product domains and Fuglede's conjecture for convex polytopes ⋮ Isospectral measures ⋮ Spectrum is periodic for \(n\)-intervals ⋮ Spectrality of self-affine measures and generalized compatible pairs ⋮ Momentum operators in the unit square ⋮ Spectral sets and weak tiling ⋮ Tiling and spectrality for generalized Sierpinski self-affine sets ⋮ The structure of translational tilings in $\mathbb{Z}^d$ ⋮ Spectrality of Moran measures with four-element digit sets ⋮ Fourier Bases and Fourier Frames on Self-Affine Measures ⋮ Spectra for cubes in products of finite cyclic groups ⋮ Momentum operators in two intervals: spectra and phase transition ⋮ On a characterization of spectra and tilings. ⋮ Spectra of certain types of polynomials and tiling of integers with translates of finite sets. ⋮ Extension of positive definite functions ⋮ Ergodic scales in fractal measures ⋮ Uniformity of spectral self-affine measures ⋮ Fuglede’s conjecture for a union of two intervals ⋮ Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives ⋮ Frame spectral pairs and exponential bases ⋮ Continuous and discrete Fourier frames for fractal measures ⋮ Spectral measures generated by arbitrary and random convolutions ⋮ Non-spectral problem for a class of planar self-affine measures ⋮ Orthogonal harmonic analysis of fractal measures ⋮ A note on Gabor orthonormal bases ⋮ The structure of cube tilings under symmetry conditions ⋮ On the \(\mu_{M,D}\)-orthogonal exponentials ⋮ Families of spectral sets for Bernoulli convolutions ⋮ Duality properties between spectra and tilings ⋮ Orthogonal exponentials, translations, and Bohr completions ⋮ Quasiperiodic spectra and orthogonality for iterated function system measures ⋮ 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 ⋮ Fourier duality for fractal measures with affine scales ⋮ Fuglede's conjecture holds in \(\mathbb{Q}_p\) ⋮ Spectral theory of multiple intervals ⋮ Iterated function systems, Ruelle operators, and invariant projective measures ⋮ Wavelets, tiling, and spectral sets ⋮ On spectral Cantor measures ⋮ Mock Fourier series and transforms associated with certain Cantor measures ⋮ Translation representations and scattering by two intervals ⋮ Orthogonality relations on certain homogeneous spaces

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