Representation of differential operators in wavelet basis

M. A. Hajji, S. Melkonian, R. Vaillancourt

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂x and ∂y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂x, ∂y) is derived, where g is an analytic function.

Original languageEnglish
Pages (from-to)1011-1033
Number of pages23
JournalComputers and Mathematics with Applications
Issue number6-7
Publication statusPublished - 2004
Externally publishedYes


  • Block circulant
  • Circulant
  • Partial-differential operator
  • Wavelet

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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