Bessel-type operators with an inner singularity

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Langer, Heinz and Langer, Matthias 2013. Bessel-type operators with an inner singularity. Integral Equations and Operator Theory 75 (2) , pp. 257-300. 10.1007/s00020-012-2023-3

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Abstract

We consider a Bessel-type differential expression on [0, a], a > 1, with the singularity at the inner point x = 1, see (1.2) below. This singularity is in the limit point case from both sides. Therefore in a Hilbert space treatment in L2(0, a), e.g. for Dirichlet boundary conditions at x = 0 and x = a, a unique self-adjoint operator is associated with this differential expression. However, in papers by J. F. van Diejen and A. Tip, Yu. Shondin, A. Dijksma, P. Kurasov and others, in more general situations, self-adjoint operators in some Pontryagin space were connected with this kind of singular equations; for (1.2) this connection appeared also in the study of a continuation problem for a hermitian function by H. Langer, M. Langer and Z. Sasv´ari. In the present paper we give an explicit construction of this Pontryagin space for the Besseltype equation (1.2) and a description of the self-adjoint operators which can be associated with it.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher:	Springer Verlag
ISSN:	0378-620X
Funders:	Leverhulme Trust
Last Modified:	24 Oct 2022 10:10
URI:	https://orca.cardiff.ac.uk/id/eprint/43342

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