Bispectrality and Time–Band Limiting: Matrix-valued Polynomials
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 20, 2018
- Source ID
- 10.1093/imrn/rny140
Entities
People
- F. Alberto Grünbaum
- Ignacio Zurrián
- Inés Pacharoni
Organizations
- Air Force Office of Scientific Research
- National Fund for Scientific and Technological Development
- National Scientific and Technical Research Council
- National University of Córdoba