Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

Continuations of Hermitian indefinite functions and corresponding canonical systems: an example

Langer, H. and Langer, M. and Sasvari, Z. (2004) Continuations of Hermitian indefinite functions and corresponding canonical systems: an example. Methods of Functional Analysis and Topology, 10 (1). pp. 39-53. ISSN 1029-3531

[img]
Preview
PDF (strathprints002184.pdf)
strathprints002184.pdf

Download (282kB) | Preview

Abstract

M. G. Krein established a close connection between the continuation problem of positive definite functions from a finite interval to the real axis and the inverse spectral problem for differential operators. In this note we study such a connection for the function f(t) = 1 − |t|, t - R, which is not positive definite on R: its restrictions fa := f|(−2a,2a) are positive definite if a ≤ 1 and have one negative square if a > 1. We show that with f a canonical differential equation or a Sturm-Liouville equation can be associated which have a singularity.