Picture of smart phone in human hand

World leading smartphone and mobile technology research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by Strathclyde researchers from the Department of Computer & Information Sciences involved in researching exciting new applications for mobile and smartphone technology. But the transformative application of mobile technologies is also the focus of research within disciplines as diverse as Electronic & Electrical Engineering, Marketing, Human Resource Management and Biomedical Enginering, among others.

Explore Strathclyde's Open Access research on smartphone technology now...

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

Langer, Heinz and Langer, Matthias and Sasvári, Zoltán (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
Text (strathprints002184)
strathprints002184.pdf - Accepted Author Manuscript

Download (218kB) | 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.