Book chapter
Fourier series on fractals: a parallel with wavelet theory
Radon transforms, geometry, and wavelets: AMS Special Session, January 7-8, 2007, New Orleans, Louisiana : Workshop, January 4-5, 2007, Baton Rouge, Louisiana, pp.75-101
Contemporary mathematics, 464, Providence, R.I.
2008
Abstract
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces L2 (μ) with measures μ arising from iterated function systems (IFS). This includes equilibrium measures in complex dynamics. Motivated by applications, we draw parallels between analysis of fractal measures on the one hand, and the geometry of wavelets on the other. We are motivated by spectral theory for commuting partial differential operators and related duality notions. While stated initially for bounded and open regions in Rd, they have since found reformulations in the theory of fractals and wavelets. We include a historical sketch with questions from early operator theory.
Details
- Title: Subtitle
- Fourier series on fractals: a parallel with wavelet theory
- Creators
- Dorin Ervin DutkayPalle E T Jorgensen - University of Iowa, Mathematics
- Resource Type
- Book chapter
- Publication Details
- Radon transforms, geometry, and wavelets: AMS Special Session, January 7-8, 2007, New Orleans, Louisiana : Workshop, January 4-5, 2007, Baton Rouge, Louisiana, pp.75-101
- Publisher
- Providence, R.I.; American Mathematical Society
- Series
- Contemporary mathematics; 464
- Language
- English
- Date published
- 2008
- Academic Unit
- Mathematics
- Record Identifier
- 9983985964802771
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