Wavelet frames with Laguerre functions

Abreu, Luis Daniel

doi:10.1016/j.crma.2011.02.013

Complex Analysis/Theory of Signals

Wavelet frames with Laguerre functions
[Frames dʼondelettes et fonctions de Laguerre]

Présenté par : the Editorial Board

Abreu, Luis Daniel ¹

¹ CMUC, Departamento de Matemática da Universidade de Coimbra, 3001-454 Coimbra, Portugal

Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 255-258.

Résumé
Abstract

Soit le fonction $Φ_{n}^{α}$ de la forme $F Φ_{n}^{α} (t) = t^{\frac{1}{2}} l_{n}^{α} (2 t)$ , ou $l_{n}^{α}$ est une fonction de Laguerre et $Γ (a, b) = {(a^{m} b k, a^{m})}_{k, m \in Z}$ est une reseau hyperbolique. Notre resultat principal dit que, si lʼ ensemble dʼondelettes $W (Φ_{n}^{α}, Γ (a, b))$ est un frame pour $H^{2} (C^{+})$ , alors, $b \log a < 4 π \frac{n + 1}{α + 1}$ .

Consider the functions $Φ_{n}^{α}$ defined as $F Φ_{n}^{α} (t) = t^{\frac{1}{2}} l_{n}^{α} (2 t)$ , where $l_{n}^{α}$ is a Laguerre function and $Γ (a, b) = {(a^{m} b k, a^{m})}_{k, m \in Z}$ is a hyperbolic lattice. We prove that, if the wavelet system $W (Φ_{n}^{α}, Γ (a, b))$ is a frame of $H^{2} (C^{+})$ , then $b \log a < 4 π \frac{n + 1}{α + 1}$ .

Reçu le : 2010-01-21
Accepté le : 2011-02-14
Publié le : 2011-02-24

DOI : 10.1016/j.crma.2011.02.013

Affiliations des auteurs :

Abreu, Luis Daniel ¹

¹ CMUC, Departamento de Matemática da Universidade de Coimbra, 3001-454 Coimbra, Portugal

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     title = {Wavelet frames with {Laguerre} functions},
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Abreu, Luis Daniel. Wavelet frames with Laguerre functions. Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 255-258. doi : 10.1016/j.crma.2011.02.013. https://www.numdam.org/articles/10.1016/j.crma.2011.02.013/

Bibliographie
Cité par

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[2] L.D. Abreu, Beurling type density theorems for polyanalytic functions in the unit disc, in preparation.

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Abreu, Luís Daniel Superframes and Polyanalytic Wavelets, Journal of Fourier Analysis and Applications, Volume 23 (2017) no. 1, p. 1 | DOI:10.1007/s00041-015-9448-4
Abreu, L.D.; Balazs, P.; de Gosson, M.; Mouayn, Z. Discrete coherent states for higher Landau levels, Annals of Physics, Volume 363 (2015), p. 337 | DOI:10.1016/j.aop.2015.09.009
Abreu, Luis Daniel; Feichtinger, Hans G. Function Spaces of Polyanalytic Functions, Harmonic and Complex Analysis and its Applications (2014), p. 1 | DOI:10.1007/978-3-319-01806-5_1
Abreu, Luis Daniel Super-Wavelets Versus Poly-Bergman Spaces, Integral Equations and Operator Theory, Volume 73 (2012) no. 2, p. 177 | DOI:10.1007/s00020-012-1956-x

Cité par 4 documents. Sources : Crossref

^☆ This research was partially supported by CMUC/FCT and FCT project “Frame Design” PTDC/MAT/114394/2009, POCI 2010 and FSE.