Dr Ian Wood Presented a Series of Talks in Louisiana and Texas

Senior Lecturer in Mathematics, Dr Ian Wood, from the School of Mathematics, Statistics and Actuarial Science (SMSAS) at the University of Kent, presented a range of talks during a recent three-week trip to the United States of America.

During Ian’s visit, he presented a talk on ‘Boundary triples and spectral information in abstract M-functions’ at the Applied Analysis Seminar at Louisiana State University in Baton Rouge, Louisiana.

Abstract:

The Weyl-Titchmarsh m-function is an important tool in the study of forward and inverse problems for ODEs, as it contains all the spectral information of the problem. The abstract setting of boundary triples allows the introduction of an abstract operator M-function. It is then interesting to study how much spectral information is still contained in the M-function in this more general setting. Boundary triples allow for the study of PDEs, block operator matrices and many other problems in one framework. We will discuss properties of M-functions, their relation to the resolvent and the spectrum of the associated operator, and connections to the extension theory of operators.

He also presented a talk titled, ‘Embedding eigenvalues for periodic Jacobi operators using Wigner-von Neumann-type perturbations’ at the Baylor Analysis Seminar at Baylor University in Waco, Texas, and at the Applied Mathematics Seminar at the University of Texas in San Antonio, Texas.

Abstract:

We consider a method of embedding eigenvalues in a band of absolutely continuous spectrum of a periodic Jacobi operator by adding a potential. We first discuss embedding a single eigenvalue and then show that the method can be extended to allow embedding infinitely many eigenvalues into the band.