Representation Theory and Multilevel Filters

Authors

Daniel Alpay, Chapman UniversityFollow
Palle Jorgensen, University of Iowa
Izchak Lewkowicz, Ben-Gurion University of the Negev

Document Type

Article

Publication Date

10-25-2022

Abstract

We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical L²(R, dx) setting. This is done in a framework of iterated function system (IFS) measures; these include all cases studied so far, and in particular the Julia set/measure cases. Every IFS has a fixed order, say N, and we show that the wavelet filters are indexed by the infinite dimensional group G of functions from X into the unitary group U_N. We call G the loop group because of the special case of the unit circle.

Comments

This article was originally published in Journal of Applied Mathematics and Computing in 2022. https://doi.org/10.1007/s12190-022-01805-z

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Recommended Citation

Alpay, D., Jorgensen, P. & Lewkowicz, I. Representation theory and multilevel filters. J. Appl. Math. Comput. (2022). https://doi.org/10.1007/s12190-022-01805-z

Peer Reviewed

1

Copyright

Springer