FOURIER SERIES ON FRACTALS: A PARALLEL WITH WAVELET THEORY
By Dorin Ervin Dutkay, Palle E. T. Jorgensen. 2007
58 citations recorded by the source corpus.
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces L 2 (µ) with measures µ arising from iterated function systems (IFS). This includes equilibrium mea- sures 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 com- muting partial differential operators and related duality notions. While stated initially for bounded and open regions in R d , they have since found reformulations in the theory of fractals and wavelets. We include a historical sketch with questions from early operator theory.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e4fb29ffec49def2e394e24e6e4bb57194174951
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In Applied Mathematics
In Computer Vision and Pattern Recognition
In Mathematical Physics
Citations in the corpus
- Spectra of a class of self-affine measures (2011, methodology): “(C) Dutkay and Jorgensen proposed the following problem in [3, Problem 4].”