Abstract

Orthonormal wavelets are special functions used to build orthonormal bases in the space of square-integrable functions. They allow for the analysis and reconstruction of functions through operations of translation and dilation. Wavelets have a wide range of applications in science, including signal processing, digital image and audio analysis, seismology, and quantum mechanics, among others. In our research, we focus on a class of extended Gevrey regular functions, within which we successfully constructed wavelets. This is a joint work with Professor Nenad Teofanov and Professor Filip Tomić. The research was supported by the Science Fund of the Republic of Serbia, under GRANT No. 2727, titled Global and Local Analysis of Operators and Distributions – GOALS.