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. 3953. ISSN 10293531

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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 SturmLiouville equation can be associated which have a singularity.
Item type:  Article 

ID code:  2184 
Keywords:  Hermitian indefinite functions, canonical systems, SturmLiouville equation, Mathematics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Strathprints Administrator 
Date Deposited:  05 Jan 2007 
Last modified:  13 Jun 2016 04:06 
URI:  http://strathprints.strath.ac.uk/id/eprint/2184 