Journal article
Orthogonal harmonic analysis of fractal measures
Electronic research announcements of the American Mathematical Society, Vol.4(6), pp.35-42
1998
DOI: 10.1090/S1079-6762-98-00044-4
Abstract
We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis. Overview We study properties of pairs of Borel measures on R simultaneously generalizing Fourier series and the Fourier transform. We show that certain fractal measures fall within the class of measures admitting generalized Fourier series. The class of fractal measures considered in this paper are obtained from an affine iteration construction leading to self-affine measures μ with support in R. The affine maps are determined by a given expansive d × d matrix and a finite set of translation vectors. We show that the corresponding L-space L(μ) has an orthonormal basis of exponentials e λ·x, indexed by vectors λ in R, provided certain geometric conditions hold for the affine system.
Details
- Title: Subtitle
- Orthogonal harmonic analysis of fractal measures
- Creators
- Palle E.T JorgensenSteen Pedersen
- Resource Type
- Journal article
- Publication Details
- Electronic research announcements of the American Mathematical Society, Vol.4(6), pp.35-42
- DOI
- 10.1090/S1079-6762-98-00044-4
- ISSN
- 1079-6762
- eISSN
- 1079-6762
- Language
- English
- Date published
- 1998
- Academic Unit
- Mathematics
- Record Identifier
- 9983985858702771
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