NDLI: Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals

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Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals

Passive Systems with a Normal Main Operator and Quasi-selfadjoint Systems

Boundary Relations, Unitary Colligations, and Functional Models

Borel–Carathéodory Type Theorem for Monogenic Functions

Boundedness of Convolution Operators and Input–Output Maps between Weighted Spaces

On H. Weyl and J. Steiner Polynomials

The Poisson Kernel for Hardy Algebras

Operator Valued Functions with Pick Operators Having Negative Subspaces of Bounded Dimensions

Weyl–Titchmarsh Function of an Abstract Boundary Value Problem, Operator Colligations, and Linear Systems with Boundary Control

Stable Ranks of Banach Algebras of Operator-Valued Analytic Functions

Complex Analysis and Operator Theory : Volume 2

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Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals

Content Provider	Springer Nature Link
Author	Albeverio, Sergio Paolucci, Anna Maria
Copyright Year	2008
Abstract	We study Bernoulli type convolution measures on attractor sets arising from iterated function systems on R. In particular we examine orthogonality for Hankel frequencies in the Hilbert space of square integrable functions on the attractor coming from a radial multiresolution analysis on R $^{3}$. A class of fractals emerges from a finite system of contractive affine mappings on the zeros of Bessel functions. We have then fractal measures on one hand and the geometry of radial wavelets on the other hand. More generally, multiresolutions serve as an operator theoretic framework for the study of such selfsimilar structures as wavelets, fractals, and recursive basis algorithms. The purpose of the present paper is to show that this can be done for a certain Bessel–Hankel transform.
Starting Page	1
Ending Page	18
Page Count	18
File Format	PDF
ISSN	16618254
Journal	Complex Analysis and Operator Theory
Volume Number	3
Issue Number	1
e-ISSN	16618262
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2008-04-28
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hilbert spaces Cuntz algebra iterated function systems radial multiresolution Bessel functions fractals Wavelets and other special systems Other transforms and operators of Fourier type Hilbert spaces with reproducing kernels Hypergroups Operators in $C^*$- or von Neumann algebras Mathematics Operator Theory Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Theory and Mathematics Computational Mathematics

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Extremal Functions on Sturm–Liouville Hypergroups

Fractional Functions and their Representations

Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals

Translation-invariant operators in reproducing kernel Hilbert spaces

Cuntz–Krieger Algebras and Wavelets on Fractals

Applications of the work of Stone and von Neumann to wavelets

Symmetric Operators and Reproducing Kernel Hilbert Spaces

Radial multiresolution, Cuntz algebras representations and an application to fractals

Hyperholomorphic Bergman Spaces and Bergman Operators Associated with Domains in $${\mathbb{C}}^2$$

Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals

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