Composite Wavelet Transforms: Applications and Perspectives

Autor:	Aliev, Ilham A., Rubin, Boris, Sezer, Sinem, Uyhan, Simten B.
Rok vydání:	2007
Předmět:	Mathematics - Functional Analysis 42C40 44A12 47G10
Druh dokumentu:	Working Paper
Popis:	We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the relevant Calder\'{o}n-type reproducing formulas constitute a unified approach to explicit inversion of the Riesz, Bessel, Flett, parabolic and some other operators of the potential type generated by ordinary (Euclidean) and generalized (Bessel) translations. This approach is exhibited in the paper. Another concern is application of the composite wavelet transforms to explicit inversion of the k-plane Radon transform on $\bbr^n$. We also discuss in detail a series of open problems arising in wavelet analysis of $L_p$-functions of matrix argument. Comment: 25 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0711.1424 Zobrazit plný text záznamu View this record from Arxiv