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
and in the case of
being the closure of a -lattice with -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
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.