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Full-Text Articles in Physical Sciences and Mathematics
The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall
The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall
Honors Theses
One can see that this matrix is unitary and has eigenvalues {1,−i,−1, I}, each of infinite multiplicity. Throughout the remainder of this thesis, we will convince the reader that the above linear transformation is actually the Fourier transform. We will compute the commutant, as well as its invariant subspaces. The key to do this relies on the Hermite polynomials. Why do we recast the Fourier transform from its well-known and well studied integral form to the matrix form shown above? As we will see, the matrix form allows us to efficiently discover the operator theory of the Fourier transform obfuscated …
Solving The Yang-Baxter Matrix Equation, Mallory O. Jennings
Solving The Yang-Baxter Matrix Equation, Mallory O. Jennings
Honors Theses
The Yang-Baxter equation is one that has been widely used and studied in areas such as statistical mechanics, braid groups, knot theory, and quantum mechanics. While many sets of solutions have been found for this equation, it is still an open problem. In this project, I solve the Yang-Baxter matrix equation that is similar in format to the Yang-Baxter equation. I try to solve the corresponding Yang-Baxter matrix equation, ������=������, where X is an unknown ������ matrix, and ��=[0����0] or [0−��−��0], by using the Jordan canonical form to find infinitely many solutions.