Shift invariant spaces are common in the study of analysis, appearing, for example, as cornerstones of the theories of wavelets and sampling. The interplay of these three notions is discussed at length over R, with the one-dimensional study providing motivation for later discussions of Rn, locally compact abelian groups, and some non-abelian groups. Two fundamental tools, the so-called bracket" as well as the Zak transform(s), are described, and their deep connections to the aforementioned areas of study are made explicit.

Date Published: 26 September 2013
PDF: 9 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 885808 (26 September 2013); doi: 10.1117/12.2028784

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)