Abstract:
Wavelet theory constitutes a recent and very active area of mathematics which has been used successfully in several fields of research, such as, pattern recognition, analysis, data compression, quantum physics and acoustics, etc., embracing, therefore, areas from pure and applied mathematics to physics, computation and engineering. An important question in this theory is the application of an operator, represented in a certain wavelet basis (adequately chosen), to an arbitrary function. The representation of the operator can be done in two distinct forms: standard and non-standard. The main purpose of this thesis is the study and detailed description of the standard and non-standard representations of operators. We will show, in particular, how these representations can be used to compress certain classes of operators. The representation of some particular examples of operators will be explicitly constructed and the respective compression rates will be numerically computed. Finally, some applications of these representations will be reported.

Uso de ôndulas na compressão de operadores (pdf) »»