Picture of a sphere with binary code

Making Strathclyde research discoverable to the world...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. It exposes Strathclyde's world leading Open Access research to many of the world's leading resource discovery tools, and from there onto the screens of researchers around the world.

Explore Strathclyde 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.