A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Selfadjoint Jacobi matrices on graphs and multiple orthogonal polynomials”, Keldysh Institute preprints, 2018,003, 27 pp.

This article is cited in 1 paper

Selfadjoint Jacobi matrices on graphs and multiple orthogonal polynomials

A. I. Aptekarev^a, S. A. Denisov^ab, M. L. Yattselev^c

^a Keldysh Institute of Applied Mathematics, Russian Academy of Science, Moscow, Russian Federation
^b Department of Mathematics, University of Wisconsin-Madison, 480nLincoln Dr., Madison, WI 53706, USA
^c Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 North Blackford Street, Indianapolis, IN 46202, USA

Abstract: Selfadjoint operators on the graph-trees are constructed by means of the difference equations connecting nearest neighbors in the lattice of multiple orthogonal polynomials. This construction generalizes the Jacobi matrices of the recurrence relations for orthogonal polynomials.

Keywords: difference operators on graphs; multiple orthogonal polynomials; discrete integrable systems; spectral and scattering problem.

DOI: 10.20948/prepr-2018-3