Abstract
Abstract
The time and band limiting operator is introduced to optimize the reconstruction of a signal from only a partial part of its spectrum. In the discrete case, this operator commutes with the so-called algebraic Heun operator which appears in the context of the quantum integrable systems. The construction of both operators and the proof of their commutativity is recalled. A direct connection between their spectra is obtained. Then, the Bethe ansatz, a well-known method to diagonalize integrable quantum Hamiltonians, is used to diagonalize the Heun operator and to obtain insights on the spectrum of the time and band limiting operator.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
2 articles.
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1. A new commutativity property of exceptional orthogonal polynomials;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2024-03-29
2. Bethe ansatz diagonalization of the Heun–Racah operator;Letters in Mathematical Physics;2023-01-17