Physical Sciences and Mathematics Commons^™

The Complete Structure Of Linear And Nonlinear Deformations Of Frames On A Hilbert Space, Devanshu Agrawal

Electronic Theses and Dissertations

A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show …