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Articles 1 - 3 of 3
Full-Text Articles in Harmonic Analysis and Representation
Parametrizing Finite Frames And Optimal Frame Completions, Miriam J. Poteet
Parametrizing Finite Frames And Optimal Frame Completions, Miriam J. Poteet
Theses and Dissertations
Frames are used in many signal processing applications. We consider the problem of constructing every frame whose frame operator has a given spectrum and whose vectors have prescribed lengths. For a given spectrum and set of lengths, we know when such a frame exists by the Schur-Horn Theorem; it exists if and only if its spectrum majorizes its squared lengths. We provide a more constructive proof of Horn's original result. This proof is based on a new method for constructing any and all frames whose frame operator has a prescribed spectrum and whose vectors have prescribed lengths. Constructing all such …
Ramanujan Sums As Supercharacters, Christopher F. Fowler '12, Stephan Ramon Garcia, Gizem Karaali
Ramanujan Sums As Supercharacters, Christopher F. Fowler '12, Stephan Ramon Garcia, Gizem Karaali
Pomona Faculty Publications and Research
The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality.
Semigroup As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy
Semigroup As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors study the zero divisor graph and unit graph of a semigroup. The zero divisor graphs of semigroups Zn under multiplication is studied and characterized.