CONICET | Buscador de Institutos y Recursos Humanos

The subject of time-band-limiting, originating in signal processing, is dominated by themiracle that a naturally appearing integral operator admits a commuting differential one allowingfor a numerically efficient way to compute its eigenfunctions. Bispectrality is an effort to dig intothe reasons behind this miracle and goes back to joint work with H. Duistermaat. This search hasrevealed unexpected connections with several parts of mathematics, including integrable systems.Here we consider a matrix valued version of bispectrality and give a general condition underwhich we can display a constructive and simple way to obtain the commuting dierential operator.Furthermore, we build an operator that commutes with both the time-limiting operator and theband-limiting operators.