A PONTRYAGIN SPACE APPROACH TO SINGULAR PERTURBATIONS OF DIFFERENTIAL OPERATORS

HEINZ LANGER

hlanger@mail.zserv.tuwien.ac.at

Institute for Analysis and Technical Mathematics

Technical University of Vienna

Wiedner Hauptstr. 8-10, A-1040 Vienna, Austria

Technical University of Vienna

Wiedner Hauptstr. 8-10, A-1040 Vienna, Austria

In the study of singularly perturbed differential
expressions operators of the form
arise, where is a
self-adjoint operator in some Hilbert space
and
is some element of a space with negative norm
(
)
associated with . Recently, by Yu. Shondin and J.F. van
Diejen/A.Tip a method was developed which associates with the
problem a family of operators in some Pontryagin space with
negative index which are extensions of a symmetric operator in
the given Hilbert space. In the lecture an analytic approach to
these extensions using the -function or Titchmarsh-Weyl
function will be explained. The method applies also e.g. to the
Bessel operator
in
the self-adjoint case , if the -function from the
non-self-adjoint case is considered for such values
. Joint work with Y. Shondin and A. Dijksma.

EPSRC Gregynog Workshop, 21-26 July 2002