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math.CA2026
A Riemann-Hilbert approach to the computation of transform pairs
Kaitlynn Lilly, Thomas Trogdon
We develop a unified methodology that integrates spectral theory, Riemann-Hilbert problems, and inverse scattering theory for the construction and numerical evaluation of transform…
math.SP2026
Banded Hermitian Matrices, Matrix Orthogonal Polynomials, and the Toda Lattice
Charbel Abi Younes, Thomas Trogdon
We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure…