On the structure of the space of wavelet transforms

Hutník, Ondrej

doi:10.1016/j.crma.2008.04.013

Functional Analysis

On the structure of the space of wavelet transforms
[Sur l'structure de espace des transformées en ondelette]

Présenté par : Yves Meyer

Hutník, Ondrej ¹

¹ Institute of Mathematics, Faculty of Science, P.J. Šafárik University in Košice, Jesenná 5, 04154 Košice, Slovakia

Comptes Rendus. Mathématique, Tome 346 (2008) no. 11-12, pp. 649-652.

Résumé
Abstract

Soient G le groupe affine « $a x + b$ », dν une mesure de Haar invariante à gauche sur G et ψ une ondelette réelle admissible dans $L_{2} (R)$ . La décomposition complète de $L_{2} (G, d ν)$ sur les espaces des transformées en ondelette $W_{ψ} (L_{2} (R))$ est obtenue, par l'identification du groupe G avec le demi-plan supérieur Π dans $C$ .

Let G be the “ $a x + b$ ”-group with the left invariant Haar measure dν and ψ be a fixed real-valued admissible wavelet on $L_{2} (R)$ . The complete decomposition of $L_{2} (G, d ν)$ onto the space of wavelet transforms $W_{ψ} (L_{2} (R))$ is obtained after identifying the group G with the upper half-plane Π in $C$ .

Reçu le : 2007-07-31
Accepté le : 2008-04-23
Publié le : 2008-05-20

DOI : 10.1016/j.crma.2008.04.013

Affiliations des auteurs :

Hutník, Ondrej ¹

¹ Institute of Mathematics, Faculty of Science, P.J. Šafárik University in Košice, Jesenná 5, 04154 Košice, Slovakia

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Hutník, Ondrej. On the structure of the space of wavelet transforms. Comptes Rendus. Mathématique, Tome 346 (2008) no. 11-12, pp. 649-652. doi : 10.1016/j.crma.2008.04.013. https://www.numdam.org/articles/10.1016/j.crma.2008.04.013/

Bibliographie
Cité par

[1] Calderón, A. Intermediate spaces and interpolation, the complex method, Studia Math., Volume 24 (1964), pp. 113-190

[2] Grossmann, A.; Morlet, J.; Paul, T. Transforms associated to square integrable group representations II: Examples, Ann. Inst. Henri Poincaré, Volume 45 (1986), pp. 293-309

[3] O. Hutník, On Toeplitz-type operators related to wavelets, Integral Equations Operator Theory, submitted for publication

[4] Klauder, J.R.; Skagerstam, B. Coherent States, Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985

[5] Nowak, K. Weak type estimates for singular values of commutators on weighted Bergman spaces, Indiana Univ. Math. J., Volume 40 (1991), pp. 1315-1331

[6] Nowak, K. Commutators based on the Calderón reproducing formula, Studia Math., Volume 104 (1993) no. 3, pp. 285-306

[7] T. Paul, États quantiques réalisés pas des fonctions analytiques dans le demi-plan, Thèse de 3ième cycle, Université Pierre et Marie Curie, 1984

[8] Paul, T. Functions analytic on the half-plane as quantum mechanical states, J. Math. Phys., Volume 25 (1984), pp. 3252-3262

[9] Vasilevski, N.L. On the structure of Bergman and poly-Bergman spaces, Integral Equations Operator Theory, Volume 33 (1999), pp. 471-488

Wang, Xia; Shi, Yanyue; Zhang, Bo; Wei, Changguo; Bilalov, Bilal The Zero Product of Toeplitz Operators on the 2‐Analytic Weighted Bergman Space, Journal of Function Spaces, Volume 2025 (2025) no. 1 | DOI:10.1155/jofs/4435105
Barrera-Castelán, Roberto Moisés; Maximenko, Egor A.; Ramos-Vazquez, Gerardo Radial operators on polyanalytic weighted Bergman spaces, Boletín de la Sociedad Matemática Mexicana, Volume 27 (2021) no. 2 | DOI:10.1007/s40590-021-00348-w
Maximenko, Egor A.; Tellería-Romero, Ana María Radial Operators on Polyanalytic Bargmann–Segal–Fock Spaces, Operator Algebras, Toeplitz Operators and Related Topics, Volume 279 (2020), p. 277 | DOI:10.1007/978-3-030-44651-2_18
Hutníková, Mária; Mišková, Anna Continuous Stockwell transform: Coherent states and localization operators, Journal of Mathematical Physics, Volume 56 (2015) no. 7 | DOI:10.1063/1.4926950
Hutníková, Mária On the range of Stockwell transforms, Applied Mathematics and Computation, Volume 219 (2013) no. 17, p. 8904 | DOI:10.1016/j.amc.2013.03.028
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
Hutník, Ondrej On Boundedness of Calderón–Toeplitz Operators, Integral Equations and Operator Theory, Volume 70 (2011) no. 4, p. 583 | DOI:10.1007/s00020-011-1883-2
Hutník, Ondrej Wavelets from Laguerre Polynomials and Toeplitz-Type Operators, Integral Equations and Operator Theory, Volume 71 (2011) no. 3, p. 357 | DOI:10.1007/s00020-011-1907-y
Abreu, Luís Daniel Sampling and interpolation in Bargmann–Fock spaces of polyanalytic functions, Applied and Computational Harmonic Analysis, Volume 29 (2010) no. 3, p. 287 | DOI:10.1016/j.acha.2009.11.004
Hutník, Ondrej A note on wavelet subspaces, Monatshefte für Mathematik, Volume 160 (2010) no. 1, p. 59 | DOI:10.1007/s00605-008-0084-9
Abreu, Luís Daniel On the structure of Gabor and super Gabor spaces, Monatshefte für Mathematik, Volume 161 (2010) no. 3, p. 237 | DOI:10.1007/s00605-009-0177-0

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