Time and Band Limiting for Exceptional Orthogonal Polynomials

Explore the fascinating world of time-and-band limiting in this 57-minute lecture by F. Alberto Grünbaum at the Centre de recherches mathématiques (CRM). Delve into the historical origins of this phenomenon, tracing back to the work of Slepian, Landau, and Pollak at Bell Labs in the 1960s. Discover the intriguing connections between integral operators and differential operators, and learn how the concept extends beyond traditional Fourier analysis. Investigate the bispectral problem and its surprising links to the KdV equation, master symmetries, and monodromy. Examine the contributions of various mathematicians to the field, including extensions to matrix-valued cases and discrete-continuous scenarios. Uncover the relationships between time-and-band limiting and random matrix theory, exceptional orthogonal polynomials, and recent developments in connection with Riemann's zeta function and the Bethe Ansatz. Gain insights into ongoing research projects and potential future directions in this captivating area of mathematics.