Indefinite Generalizations of Canonical Systems View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2002-2006

FUNDING AMOUNT

N/A

ABSTRACT

A classical canonical system in this project is a special symmetric first order system of two ordinary lineardifferential equations which has locally summable coefficients and depends linearly on the spectral parameter. Thespectral properties of such a system are completely determined by its Titchmarsh-Weyl coefficient, which is ananalytic function mapping the upper half plane into itself, or, equivalently, for which a certain kernel is positivedefinite. The inverse spectral problem consists in the reconstruction of the canonical system from a givenTitchmarsh-Weyl coefficient. In the classical situation its solution is contained in the work of de Branges.During the last 30 years also systems have been considered, whose coefficients have singularities or which dependnonlinearly on the eigenvalue parameter. They lead to Titchmarsh-Weyl coefficients for which this kernel is notpositive definite but has a finite number of negative squares. The aim of the present project is to give a descriptionof a general class of canonical systems, which have a Titchmarsh-Weyl coefficient of this type. These systems areclosely related to Sturm-Liouville operators with singular potentials and floating singularities, and also to stringswith indefinite mass distribution and dipoles. More... »

URL

http://pf.fwf.ac.at/en/research-in-practice/project-finder/11181

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