Orthogonal harmonic analysis of fractal measures

DOI10.1090/S1079-6762-98-00044-4zbMath0893.28005OpenAlexW1838877444MaRDI QIDQ4387110

Steen Pedersen, Palle E. T. Jorgensen

Publication date: 6 May 1998

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/230088

zbMATH Keywords

Hilbert spacetilingfractalspectral resolutionFourier basisspectral pairself-similar measureaffine iteration

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Noncommutative dynamical systems (46L55) Length, area, volume, other geometric measure theory (28A75)

Related Items (9)

Spectrality of a class of Moran measures on with consecutive digit sets ⋮ Three-way tiling sets in two dimensions ⋮ Spectra of Bernoulli convolutions and random convolutions ⋮ Duality properties between spectra and tilings ⋮ Non-spectrality of self-affine measures on the three-dimensional Sierpinski gasket ⋮ Orthogonal exponentials, translations, and Bohr completions ⋮ Spectrality of a class of Moran measures ⋮ Probability and Fourier duality for affine iterated function systems ⋮ Mock Fourier series and transforms associated with certain Cantor measures

Cites Work

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• Spectral theory of finite volume domains in \(R^ n\).
• Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure
• Spectral pairs in Cartesian coordinates
• Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
• Harmonic analysis and fractal limit-measures induced by representations of a certain \(C^*\)-algebra
• Spectral sets and factorizations of finite abelian groups
• Commuting self-adjoint partial differential operators and a group theoretic problem
• Self-similarity in harmonic analysis
• Harmonic analysis of fractal measures
• Structure of tilings of the line by a function
• On First Order Partial Differential Operators on Bounded Regions of the Plane

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