Construction of piecewise linear wavelets

It is well known that in many areas of computational mathematics, wavelet based algorithms are becoming popular for modeling and analyzing data and for providing efficient means for hierarchical data decomposition of function spaces into mutually orthogonal wavelet spaces. Wavelet construction in more than one-dimensional setting is a very challenging and important research topic. In this thesis, we first introduce the method of constructing wavelets by using semi-wavelets. Second, we construct piecewise linear wavelets with smaller support over type-2 triangulations. Then, parameterized wavelets are constructed using the orthogonality conditions.