# Dunkl two-wavelet theory and localization operators

Dunkl two-wavelet theory and localization operators In this paper the notion of a Dunkl two-wavelet is introduced. The resolution of the identity formula for the Dunkl continuous wavelet transform is then formulated and proved. Calderón’s type reproducing formula in the context of the Dunkl two-wavelet theory is proved. The two-wavelet localization operators in the setting of the Dunkl theory are then defined. The Schatten–von Neumann properties of these localization operators are established, and for trace class localization operators, the traces and the trace class norm inequalities are presented. It is proved that under suitable conditions on the symbols and two Dunkl wavelets, the boundedness and compactness of these localization operators on $$L^{p}_{k}(\mathbb {R}^{d})$$ L k p ( R d ) , $$1 \le p \le \infty$$ 1 ≤ p ≤ ∞ . Finally typical examples of localization operators are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Pseudo-Differential Operators and Applications Springer Journals

# Dunkl two-wavelet theory and localization operators

, Volume 8 (3) – Mar 13, 2017
39 pages

/lp/springer_journal/dunkl-two-wavelet-theory-and-localization-operators-IcTj0Hey2E
Publisher
Springer International Publishing
Subject
Mathematics; Analysis; Operator Theory; Partial Differential Equations; Functional Analysis; Applications of Mathematics; Algebra
ISSN
1662-9981
eISSN
1662-999X
D.O.I.
10.1007/s11868-017-0196-x
Publisher site
See Article on Publisher Site

### Abstract

In this paper the notion of a Dunkl two-wavelet is introduced. The resolution of the identity formula for the Dunkl continuous wavelet transform is then formulated and proved. Calderón’s type reproducing formula in the context of the Dunkl two-wavelet theory is proved. The two-wavelet localization operators in the setting of the Dunkl theory are then defined. The Schatten–von Neumann properties of these localization operators are established, and for trace class localization operators, the traces and the trace class norm inequalities are presented. It is proved that under suitable conditions on the symbols and two Dunkl wavelets, the boundedness and compactness of these localization operators on $$L^{p}_{k}(\mathbb {R}^{d})$$ L k p ( R d ) , $$1 \le p \le \infty$$ 1 ≤ p ≤ ∞ . Finally typical examples of localization operators are presented.

### Journal

Journal of Pseudo-Differential Operators and ApplicationsSpringer Journals

Published: Mar 13, 2017

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