Vol. 6, No. 2, 2013

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On the geometric deformations of functions in $L^2[D]$

Luis Contreras, Derek DeSantis and Kathryn Leonard

Vol. 6 (2013), No. 2, 233–241
Abstract

We derive a formal relationship between the coefficients of a function expanded in either the Legendre basis or Haar wavelet basis, before and after a polynomial deformation of the function’s domain. We compute the relationship of coefficients explicitly in three cases: linear deformation with Haar basis, linear deformation with Legendre basis, and polynomial deformation with Legendre basis.

Keywords
wavelets, Legendre basis, geometric deformation
Mathematical Subject Classification 2010
Primary: 26
Milestones
Received: 23 February 2012
Accepted: 20 May 2013
Published: 1 September 2013

Communicated by David Royal Larson
Authors
Luis Contreras
Mathematics and Applied Physics
California State University, Channel Islands
Camarillo, CA 93012
United States
Derek DeSantis
Mathematics and Applied Physics
University of Nebraska, Lincoln
Lincoln, NE 68521
United States
Kathryn Leonard
Department of Mathematics
California State University, Channel Islands
1 University Dr
Camarillo, CA 93012
United States