new method of constructing compact wavelet functions

In the thesis was examined relationship between Wavelet matrices and Wavelet functions. The proof of the main theorem, that there exists exactly one system of wavelet functions for every wavelet matrix, could not be found in a complete form, without missing parts and unproven details. In the thesis it is given completely detailed proof. During proof is constructed iterating process which is weakly convergent to a scaling function with square norm. In the second part of the thesis it is given algorithm which helps to construct Wavelet function according to Wavelet matrix. In programming language C++ was written the program and using it, there are given plots of Daubechies and several high-dimension wavelets.

Lecture files: