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, Vol. 03, No. 02: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Chair of Mathematics of Information Processing
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0219-6913
• Language: English