Wavelet and Gabor Frames on Local Fields

Wavelet theory lies at the intersection of pure and computational mathematics, as well as of audio and graphics signal processing, including compression and transmission of information. Wavelet bases have several advantages compared with other bases used as approximation tools. One of them is the so-called time-frequency localization property: Wavelet basis functions as well as their Fourier transformations rapidly decay at infinity. Through this property, in the decomposition into the basis of signals, frequency characteristics of which vary according to time or space, many expansion coefficients with unnecessary at this spatial or temporal area harmonics are small and can be discarded, thereby providing data compression. Wavelet frames are actively used for the same purposes. In the recovery of missing data from incomplete and/or damaged and noisy samples, application of wavelet methods based on frames is more advanced due to the redundancy of frame systems. This book is devoted to the development of wavelet and Gabor frames on local fields.