Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Spectral Analysis of Jacobi Matrices and
Orthogonal Polynomials

by
Professor Mourad E. H. Ismail
Department of Mathematics, University of Central Florida, USA

Date: May 4, 2005 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: We explore the connection between the spectral theory of Jacobi matrices and the moment problem. A Jacobi matrix is a matrix with zeros everywhere except possibly on the main diagonal and one diagonal above it and one below it. It acts on L 2 as a difference operator and it is indeed a discrete Schrodinger operator. We will discuss a particular example of a symmetric Jacobi operator with zero entries on the diagonal and where the entries on the other diagonals grow exponentially. In the background there is an interesting set of orthogonal polynomials which also solves a Sturm-Liouville problem involving the Askey-Wilson operator. The asymptotics of the orthogonal polynomials are very interesting and display unusual phenomena.

(Tea, coffee and cookies will be provided at the Faculty Common Room in B6501 before the colloquium from 4:00 to 4:30 pm. Please come and join us!)

** All interested are welcome **

For enquiry: 2788-9816

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