Comprehensive textbook examining meaningful connections between the subjects of Lie theory, differential geometry, and signal analysis
A Bridge Between Lie Theory and Frame Theory serves as a bridge between the areas of Lie theory, differential geometry, and frame theory, illustrating applications in the context of signal analysis with concrete examples and images.
The first part of the book gives an in-depth, comprehensive, and self-contained exposition of differential geometry, Lie theory, representation theory, and frame theory. The second part of the book uses the theories established in the early part of the text to characterize a class of representations of Lie groups, which can be discretized to construct frames and other basis-like systems. For instance, Lie groups with frames of translates, sampling, and interpolation spaces on Lie groups are characterized.
A Bridge Between Lie Theory and Frame Theory includes discussion on:
- Novel constructions of frames possessing additional desired features such as boundedness, compact support, continuity, fast decay, and smoothness, motivated by applications in signal analysis
- Necessary technical tools required to study the discretization problem of representations at a deep level
- Ongoing dynamic research problems in frame theory, wavelet theory, time frequency analysis, and other related branches of harmonic analysis
A Bridge Between Lie Theory and Frame Theory is an essential learning resource for graduate students, applied mathematicians, and scientists who are looking for a rigorous and complete introduction to the covered subjects.
Table of Content
Preface ix
Acknowledgements xi
1 Introduction 1
2 Differential Manifolds 21
3 Lie Theory 83
4 Representation Theory 173
5 Frame Theory 207
6 Frames on Eucidean Spaces 221
7 Frames on Lie Groups 241
8 Frames on Homogenous Spaces 277
9 Groups of Frames with Translates 303
10 Sampling and Interpolation on Unimodular Lie Groups 317
11 Finite Frames Maximally Robust to Erasures 351
References 367
Index 369
About the author
Vignon Oussa, Ph D, is Professor of Mathematics at Bridgewater State University in Bridgewater, MA, USA. Dr. Oussa received his Ph D in Mathematics from Saint Louis University. His areas of specialty are harmonic analysis, Lie theory, and representation theory. He is the winner of the 2014–2015 Bridgewater State University Distinguished Faculty Research Award.
More ebooks from the same author(s) / Editor
2,303 Ebooks in this category
