MS (Master of Science)
Date of Award
Committee Chair or Co-Chairs
Anant Godbole, Michelle Joyner, Debra Knisley
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 that all such frames are connected by transformations that are linear in the larger Hilbert space of square-integrable functions on the indexing space. We apply our results to frames on finite-dimensional Hilbert spaces and to the discretization of the Gabor frame with a band-limited window function.
Thesis - unrestricted
Agrawal, Devanshu, "The Complete Structure of Linear and Nonlinear Deformations of Frames on a Hilbert Space" (2016). Electronic Theses and Dissertations. Paper 3003. https://dc.etsu.edu/etd/3003
Copyright by the authors.