Journal of Wavelet Theory and Applications
  • Year: 2007
  • Volume: 1
  • Issue: 1

Interval wavelets adapted to monomial differential operators

  • Author:
  • Rémi Vaillancourt1,, Victor G. Zakharov2,
  • Total Page Count: 33
  • Page Number: 31 to 63

1Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward Ave., Ottawa, ONK1N6N5, Canada.

2Laboratory of Nonlinear Mechanics of Solids, Institute of Continuum Mechanics of RAS, 1, Acad. Korolyov Street, 614013, Perm, Russia.

*E-mail: remi@uottawa.ca

**E-mail: victor@icmm.ru

AMS Subject Classification: 42C40, 65T60.

Abstract

We introduce a method for constructing wavelets that form biorthogonal bases on an interval and are adapted to differential operators dK/dxK, K ∈ ℕ, in the sense that they diagonalize the operator matrix. The method provides an algorithm to construct the masks of the biorthogonal operator-adapted wavelets from the masks of given orthonormal wavelets. Operator-adapted wavelets satisfy homogeneous Dirichlet boundary conditions.

Keywords

Interval wavelets, biorthogonal operator-adapted wavelets, monomial differential operators, homogeneous boundary conditions, constructive methods