Construction of Globally Continuous Biorthogonal Wavelet Bases on Domains in R2

Helmut Harbrecht
Fakultät f\"ur Mathematik,
Technische Universität Chemnitz, Germany


In order to solve partial differential equations or boundary integral equations with a conforming Wavelet-Galerkin-Scheme, globally continuous biorthogonal wavelet bases are required with the following properties

In this talk we present a construction that utilizes a domain decomposition strategy. A biorthogonal wavelet system is construcuted where the biorthogonality is given with respect to a modified scalar product. These basis functions are shown satisfy the properties mentioned above.