Frames and applications: distribution of frame coeficients, integer frames and phase retrieval
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The present dissertation is divided into two main areas: frame theoretic results and applications of frames. In particular, the beginning half develops the first detailed theory of the distribution of frame coefficients. Next, the first systematic study of integer frames is included. The latter half of the dissertation is concerned with the application of frames to the area of signal reconstruction. In particular, phase retrieval by subspaces components and norm retrieval are discussed.