CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
Phone +(386) (2) 2355 350 and 2355 351 $\bullet$ Fax +(386) (2) 2355 360
Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoreticno fiziko

Fixing the Ladder Operators on Two Types of Hermite Functions

Dr. Andreas Ruffing

Technische Universität München, Zentrum Mathematik
Boltzmannstrasse 3, D-85747 Garching, Germany

Abstract Hermite Functions and their generalizations are addressed within the framework of time scale calculus on two different time scale structures. A ladder operator formalism is presented in both cases. The main focus of the article is elucidated: The ladder operator formalism is exhibited as a tool for determining orthogonality measures to recursive systems of polynomials. This procedure is performed in the case of ${\bf T} = {\bf R}$ and in the case of ${\bf T}$ being the closure of a $q$-lattice with ${\bf Z}$-grading. The main differences between the continuous and the discrete scenario are worked out. From the spectral theoretical viewpoint, the point spectra of those symmetric operators are determined to which the Hermite functions resp. their generalizations are eigenfunctions.

Seminarsko predavanje bo v torek, 1. aprila 2003 ob 15:15 uri v seminarski sobi CAMTP, Krekova 2, pritlicje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --