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...
| Autores: | , , |
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| 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 |
| 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. |
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