Construction of Globally Continuous Biorthogonal Wavelet Bases
on Domains in R2
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.
- norm equivalences in a certain range of Sobolev spaces,
- vanishing moments,
- approximation order,
- boundary value conditions.