Location: Zoom
https://unm.zoom.us/j/96832154356?pwd=S3BpaDd1TkNCQmN2L3lZdmVDUXdzUT09
Meeting ID: 968 3215 4356
Passcode: 31415926

 

Title: DEK-Type Orthogonal Polynomials

 

Abstract: In this talk, we revisit one of the first known examples of exceptional orthogonal polynomials that was introduced by Dubov, Eleonskii, and Kulagin in relation to nonharmonic oscillators with equidistant spectra. We analyze the DEK polynomials from the point of view of discrete Darboux transformations and providel a characterization which bypasses the differential equation that defines the DEK polynomials. This characterization leads to a family of general orthogonal polynomials with finitely many missing degrees. We then investigate which properties the DEK-type polynomials share with exceptional orthogonal polynomials, such as the behavior of zeros and completeness in the corresponding weighted L^2 space. We also discuss how to modify the classical Christoffel transformation for this family.

 

Bio: Rachel Bailey is a Ph.D. candidate in the Mathematics department at the University of Connecticut working under the supervision of Maria Gordina and Maxim Derevyagin. Her research lies in the study of orthogonal polynomials and operator theory. Additional information can be found on her homepage.