Vol. 1, No. 1, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 2, 185–365
Issue 1, 1–184

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
Other MSP Journals
Patch and crossover planar dyadic wavelet sets

A. J. Hergenroeder, Zachary Catlin, Brandon George and David R. Larson

Vol. 1 (2008), No. 1, 59–90

A single dyadic orthonormal wavelet on the plane 2 is a measurable square integrable function ψ(x,y) whose images under translation along the coordinate axes followed by dilation by positive and negative integral powers of 2 generate an orthonormal basis for 2(2). A planar dyadic wavelet set E is a measurable subset of 2 with the property that the inverse Fourier transform of the normalized characteristic function 1 2πχ(E) of E is a single dyadic orthonormal wavelet. While constructive characterizations are known, no algorithm is known for constructing all of them. The purpose of this paper is to construct two new distinct uncountably infinite families of dyadic orthonormal wavelet sets in 2. We call these the crossover and patch families. Concrete algorithms are given for both constructions.

wavelet, wavelet set, patch, crossover, congruence
Mathematical Subject Classification 2000
Primary: 47A13, 42C40, 42C15
Received: 26 November 2007
Accepted: 12 December 2007
Published: 28 February 2008

Communicated by Kenneth S. Berenhaut
A. J. Hergenroeder
Department of Mathematics
Davidson College
Box 5677
Davidson, NC 28035
United States
Zachary Catlin
Department of Mathematics
Purdue University
West Lafayette, IN 47907
United States
Brandon George
Department of Mathematics
University of Tennessee
Knoxville, TN 37996
United States
David R. Larson
Department of Mathematics
Texas A&M University
College Station, TX 77843-3368
United States