Orthogonal harmonie analysis and scaling of fractal measures
نویسندگان
چکیده
منابع مشابه
Orthogonal Harmonic Analysis of Fractal Measures
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...
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We show that certain iteration systems lead to fractal measures admitting exact orthogonal harmonic analysis.
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We consider aane systems in R n constructed from a given integral invertible and expansive matrix R, and a nite set B of translates, b x := R ?1 x + b; the corresponding measure on R n is a probability measure and xed by the selfsimilarity = jBj ?1 P b2B ?1 b. There are two a priori candidates for an associated orthogonal harmonic analysis : (i) the existence of some subset in R n such that the...
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ژورنال
عنوان ژورنال: Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
سال: 1998
ISSN: 0764-4442
DOI: 10.1016/s0764-4442(97)82984-9