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

Tags

Fields of Study

  • Mathematics

Readers

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