Matrix-valued commuting operators and matrix-valued spectra

GRÜNBAUM, F ALBERTO; PACHARONI, INÉS; ZURRIÁN, IGNACIO

Louvain-la-Neuve

Conferencia; Coloqium of Universite catholique de Louvain; 2018

Universite catholique de Louvain

he subject of time-band-limiting, originating in signal processing, is dominated by the ?miracle? that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its eigenfunctions. Bispectrality is an effort to dig into the reasons behind this miracle. This search has revealed unexpected connections with several parts of mathematics. In this talk consider a matrix valued version of bispectrality and give a general condition under which we can display a constructive and simple way to obtain the commuting differential operator. Furthermore, we will build an operator that commutes with both the time-limiting operator and the band-limiting operators.