#### 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
Primary: 26