Wavelet Transforms Associated to Group Representations and Functions Invariant under Symmetry Groups

Rauhut, Holger (2005): Wavelet Transforms Associated to Group Representations and Functions Invariant under Symmetry Groups. In: International Journal of Wavelets, Multiresolution and Information Processing, Bd. 03, Nr. 02: S. 167-187

Abstract

We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on ℝd.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Lehrstuhl für Mathematik der Informationsverarbeitung
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0219-6913
• Sprache: Englisch