2007/11/09 by Ilham A. Aliev, Boris Rubin, Aliev, Ilham A. +5 · 2 citations
Computer Science · Mathematics · #42C40 #44A12 #47G10 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #math.FA #msc:42C40 #msc:44A12 #msc:47G10
paper · pdf · doi:10.48550/arxiv.0711.1424
25 pages
arxiv created 2007/11/09 · openalex publication_date 2007/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Calderón-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 \bbrn. We also discuss in detail a series of open problems arising in wavelet analysis of Lp-functions of matrix argument.