Fourier series on fractals: a parallel with wavelet theory

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dc.creatorDutkay, Dorin Ervin
dc.creatorJorgensen, Palle E. T.
dc.date2007-09-17
dc.date2007-09-28
dc.date.accessioned2026-07-07T08:32:30Z
dc.date.available2026-07-07T08:32:30Z
dc.descriptionWe 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 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 $\br^d$, they have since found reformulations in the theory of fractals and wavelets. We include a historical sketch with questions from early operator theory.
dc.descriptionv2, minor correction in section 4
dc.identifierhttps://arxiv.org/abs/0709.2702
dc.identifierhttp://arxiv.org/abs/0709.2702
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138813
dc.subjectFunctional Analysis
dc.subjectDynamical Systems
dc.subject46C07, 46B99, 22D10, 13D40, 28A80, 42C40, 51F20, 37F50, 47A57, 65T60
dc.titleFourier series on fractals: a parallel with wavelet theory
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