Bispectrality and Time-Band-Limiting: Matrix valued polynomials

The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturallyappearing integral operator admits a commuting dierential one, allowing for a numerically ecient way to compute itseigenfunctions. Bispectrality is an eort to dig into the reasons behind this miracle and goes back to joint work with H.Duistermaat. This search has revealed unexpected connections with several parts of mathematics, including integrablesystems. Here we consider a matrix-valued version of bispectrality and give a general condition under which we candisplay a constructive and simple way to obtain the commuting dierential operator. Furthermore, we build an operatorthat commutes with both the time-limiting operator and the band-limiting operators.Fil: Grünbaum, Alberto. University of California at Berkeley; Estados UnidosFil: Pacharoni, Maria Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Zurrián, Ignacio Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin