The Spectrum of Self-Adjoint Extensions associated with Exceptional Laguerre Differential Expressions

Dale Frymark (TU Graz)

Nov 11. 2022, 11:30 — 12:00

The spectrum of all self-adjoint extensions for a general exceptional Laguerre-type differential expressions is given in terms of the Darboux transformations which relate the expression to the classical Laguerre differential expression in the form of an explicit Weyl--Titchmarsh m-function, up to a sign.

The construction relies primarily on boundary triples, which parameterize the self-adjoint extensions and produce the Weyl--Titchmarsh m-functions, and manipulations of Maya diagrams and partitions, which classify the seed functions defining the relevant Darboux transforms.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory of Differential Operators in Quantum Theory (Workshop)
Jussi Behrndt (TU Graz)
Fritz Gesztesy (Baylor U, Waco)
Ari Laptev (Imperial College, London)
Christiane Tretter (U Bern)