Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and application to free-slip divergence-free wavelets

This paper presents a new construction of homogeneous Dirichlet wavelet basis on the unit interval, linked by diagonal differentiation-integration relation to standard biorthogonal basis. allows compute solution Poisson equation renormalizing coefficients - as in Fourier domain but using locally supported functions with boundary conditions-, which yields linear complexity O(N) for this problem. Another application concerns free-slip divergence-free bases hypercube, general dimension, an associated decomposition algorithm simple periodic case.