Abstract

Research has shown that a frame for an n-dimensional real Hilbert space offers phase retrieval if and only if it has the complement property. There is a geometric characterization of general frames, the Han-Larson-Naimark Dilation Theorem, which gives us the necessary and sufficient conditions required to dilate a frame for an n-dimensional Hilbert space to a frame for a Hilbert space of higher dimension k. However, a frame having the complement property in an n-dimensional real Hilbert space does not ensure that its dilation will offer phase retrieval. In this thesis, we will explore and provide what necessary and sufficient conditions must be satisfied to dilate a phase retrieval frame for an n-dimensional real Hilbert space to a phase retrieval frame for a k-dimensional real Hilbert.

Thesis Completion

2018

Semester

Spring

Thesis Chair/Advisor

Han, Deguang

Degree

Bachelor of Science (B.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Pure Mathematics

Location

Orlando (Main) Campus

Language

English

Access Status

Open Access

Release Date

5-1-2018

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