Wavelet Analysis on Local Fields of Positive Characteristic [Paperback]

This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces. Local Fields.-  Multiresolution Analysis on Local Fields.- Ane, Quasi-Ane and Co-Ane Frames.-  Characterizations in Wavelet Analysis.- Biorthogonal Wavelets.- Wavelet Packets and Frame Packets.- Wavelets as Unconditional Bases.-  Shift-Invariant Spaces and Wavelets.The book provides the first systematic account of wavelets on local fields, and the authors give a clear presentation of the topics discussed. (Krishnan Parthasarathy, Mathematical Reviews, April, 2023)