A Study of Gabor Frames and Related Concepts in Banach Spaces

The book is an introductory course for theory of frames in general. The frames are discussed in Banach spaces and Hilbert spaces. Gabor frames, which are particular type of frames in a particular Hilbert space, are studied first. Various consequences of frames, like Bessel sequences and frame sequences, are considered and studied. A particular type of sequences called block sequences are defined and studied. The application of the new concept are also discussed. Frames in larger class of spaces i.e. Banach spaces, are studied. Besides many results, stability and perturbation of these concepts are also discussed. To know other similar concepts, various generalizations of frames introduced by different researchers are given. A comprehensive list of references is provided to help/assist in exploring more related to the theory of frames.