Description
Book SynopsisComprehensive 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
