On dual molecules and convolution-dominated operators |
| |
Authors: | José Luis Romero Jordy Timo van Velthoven Felix Voigtlaender |
| |
Affiliation: | 1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria;2. Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, A-1040 Vienna, Austria;3. Katholische Universität Eichstätt-Ingolstadt, Lehrstuhl Wissenschaftliches Rechnen, Ostenstraße 26, 85072 Eichstätt, Germany |
| |
Abstract: | We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size profile of its sampled values. The main tool is a local holomorphic calculus for convolution-dominated operators, valid for groups with possibly non-polynomial growth. Applied to the matrix coefficients of a group representation, our methods improve on classical results on atomic decompositions and bridge a gap between abstract and concrete methods. |
| |
Keywords: | Reproducing kernel Hilbert space Molecule Frame Convolution-dominated operators |
本文献已被 ScienceDirect 等数据库收录! |
|