Year: 2008
Type: book-chapter
Abstract: It is proved that if an interpolation map between two wavelet sets preserves the union of the sets, then the pair must be an interpolation pair. We also construct an example of a pair of wavelet sets for which the congruence domains of the associated interpolation map and its inverse are equal, and yet the pair is not an interpolation pair. The first result solves affirmatively a problem that the second author had posed several years ago, and the second result solves an intriguing problem of D. Han. The key to this counterexample is a special technical lemma on constructing wavelet sets. Several other applications of this result are also given. In addition, some problems are posed. We also take the opportunity to give some general exposition on wavelet sets and operator-theoretic interpolation of wavelets.
Source: Birkhäuser Boston eBooks
Authors: Xiaofei Zhang, David R. Larson
Institution: Texas A&M University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2113833904