Fourier frequencies in affine iterated function systems
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Publication:886121
DOI10.1016/j.jfa.2007.03.002zbMath1128.42013arXivmath/0604547OpenAlexW2042781193MaRDI QIDQ886121
Dorin Ervin Dutkay, Palle E. T. Jorgensen
Publication date: 26 June 2007
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0604547
General harmonic expansions, frames (42C15) Fractals (28A80) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Dynamical systems over complex numbers (37F99)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some properties of spectral measures
- Spectral theory of commuting self-adjoint partial differential operators
- Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure
- Mean quadratic variations and Fourier asymptotics of self-similar measures
- Dense analytic subspaces in fractal \(L^2\)-spaces
- Harmonic analysis and fractal limit-measures induced by representations of a certain \(C^*\)-algebra
- Self-affine sets and graph-directed systems
- Mock Fourier series and transforms associated with certain Cantor measures
- Commuting self-adjoint partial differential operators and a group theoretic problem
- On spectral Cantor measures
- Best choices for regularization parameters in learning theory: on the bias-variance problem.
- Fuglede's conjecture is false in 5 and higher dimensions
- Harmonic analysis of fractal measures
- Self-affine tiles in \(\mathbb{R}^n\)
- Laplacians on fractals with spectral gaps have nicer Fourier series
- Iterated function systems, Ruelle operators, and invariant projective measures
- Solution of an inverse problem for fractals and other sets
- Separation Properties for Self-Similar Sets
- [https://portal.mardi4nfdi.de/wiki/Publication:4342900 Ensembles invariants pour un op�rateur de transfert dans ? d]
- [https://portal.mardi4nfdi.de/wiki/Publication:4344721 Pavages auto-affines, op�rateurs de transfert et crit�res de r�seau dans ? d]
- On one-dimensional self-similar tilings and $pq$-tiles
- Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation
- Random iteration of analytic maps
- An Introduction to Symbolic Dynamics and Coding
- Fonctions harmoniques pour un opérateur de transition et applications
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