Vinnikov, Victor (Ben Gurion Univ.)

Overdetermined Multidimensional Systems: A Tutorial

Scheduled for presentation during the Mini-Symposium "Multidimensional Systems: Noncommutative and Overdetermined Systems II" (FrP05), Friday, July 28, 2006, 15:45−16:35, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 25, 2024

Abstract

Overdetermined multidimensional systems are systems with evolution along the multidimensional integer lattice and with - unlike the Fornasini--Marchesini model or the Roesser model - the evolution of the whole state vector specified by several separate update equations in several linearly independent directions. Because of overdeterminedness these systems come equipped with compatibility conditions for the input and output signals, yielding the transfer function which is a bundle map between flat vector bundles on a compact Riemann surface. The original motivation for the study of these systems came from operator theory (spectral analysis of tuples of nonselfadjoint and nonunitary operators) and function theory (study of meromorphic matrix valued functions on a Riemann surface, especially the analogues of the classical interpolation problems). However it seems that these systems also arise naturally in a variety of applications, from the wave-particle duality in quantum mechanics to the study of DNA chains in molecular biology. This tutorial talk will be a continuation and an update of a talk with a similar title given at MTNS 2004.