Harmonic Analysis of Fractal Measures Induced\\ by Representations of a Certain C$^*$-Algebra
نویسندگان
چکیده
منابع مشابه
Harmonic Analysis of Fractal Measures Induced by Representations of a Certain C-algebra
We describe a class of measurable subsets Ω in R such that L2(Ω) has an orthogonal basis of frequencies eλ(x) = e i2πλ·x(x ∈ Ω) indexed by λ ∈ Λ ⊂ R. We show that such spectral pairs (Ω,Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L2(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis...
متن کاملHarmonic Analysis and Fractal Limit-measures Induced by Representations of a Certain C-algebra
Palle E.T. Jorgensen and Steen Pedersen Abstra t. We describe a class of measurable subsets Ω in Rd such that L(Ω) has an orthogonal basis of frequencies eλ(x) = e (x ∈ Ω) indexed by λ ∈ Λ ⊂ Rd. We show that such spectral pairs (Ω,Λ) have a self-similarity which may be used to generate associated fractal measures μ (typically with Cantor set support). The Hilbert space L(μ) does not have a tota...
متن کاملHarmonic Analysis of Fractal Measures
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...
متن کاملOrthogonal 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...
متن کاملa comparative move analysis of the introduction sections of ma theses by iranian and native post-graduate students
since esp received universal attention to smooth the path for academic studies and productions, a great deal of research and studies have been directed towards this area. swales’ (1990) model of ra introduction move analysis has served a pioneering role of guiding many relevant studies and has proven to be productive in terms of helpful guidelines that are the outcome of voluminous productions ...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1993
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1993-00428-2