Wavelet and Gabor Frames on Local Fields

"Wavelet and Gabor Frames on Local Fields" is a specialized book that focuses on the theory of wavelets and Gabor frames in local fields. It highlights the intersections between pure and applied mathematics as well as signal processing in audio and graphics. Wavelet theory offers significant advantages over other approximation techniques, particularly due to its ability for time-frequency localization. This property allows for the identification and elimination of insignificant harmonics during signal decomposition, leading to effective data compression. The book also addresses the application of wavelet methods for recovering missing data from incomplete or damaged samples, where the redundancy of frame systems plays a crucial role. The comprehensive analysis and theoretical foundations make this work a valuable resource for students and professionals in the fields of mathematics and signal processing.