Bispectrality and Time-Band-Limiting: Matrix valued polynomials

Autor:	Grünbaum, F. Alberto, Pacharoni, Inés, Zurrián, Ignacio N.
Rok vydání:	2018
Předmět:	Mathematics - Classical Analysis and ODEs
Zdroj:	International Mathematics Research Notices, 2018, rny140
Druh dokumentu:	Working Paper
DOI:	10.1093/imrn/rny140
Popis:	The 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 and goes back to joint work with H. Duistermaat. This search has revealed unexpected connections with several parts of mathematics, including integrable systems. Here we 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 build an operator that commutes with both the time-limiting operator and the band-limiting operators. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1801.10261 Zobrazit plný text záznamu View this record from Arxiv