Irregular wavelet frames and gabor frames

Given g ∈ L^2(R^n), we consider irregular wavelet systems of the form {λ^{n/2}_j g(λ_jx − kb)}j∈Z,k∈Z^n , where λ_j > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L^2(R^n) are given. For a class of functions g ∈ L^2 (R^n) we prove that certain growth cond...

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Detalles Bibliográficos
Autores: Christensen, Ole, Favier, Sergio José, Zo, Felipe
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2001
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/118509
Acceso en línea:http://hdl.handle.net/11336/118509
Access Level:acceso abierto
Palabra clave:GROWTH CONDITION
WAVELET FRAME
GABOR FRAME
GABOR SYSTEM
WAVELET SYSTEM
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Given g ∈ L^2(R^n), we consider irregular wavelet systems of the form {λ^{n/2}_j g(λ_jx − kb)}j∈Z,k∈Z^n , where λ_j > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L^2(R^n) are given. For a class of functions g ∈ L^2 (R^n) we prove that certain growth conditions on {λ_j} will lead to frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system {e^{2πib(j,x)}g(x − λ_k}j∈Z^n, k∈Z to be a frame.