On the HELP Inequality for Hill Operators on Trees

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591 and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2012. On the HELP Inequality for Hill Operators on Trees. Brown, Brian Malcolm, Lang, Jan and Wood, Ian G., eds. Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends, Operator Theory: Advances and Applications, vol. 219. Basel: Springer, pp. 21-36. (10.1007/978-3-0348-0263-5_2)

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Abstract

The validity of a generalised HELP inequality for a Schrödinger operator with periodic potential on a rooted homogeneous tree is related to the quasi-stability or quasi-instability of the associated differential equation. A numerical approach to the determination of the optimal constant in the HELP inequality is presented. Moreover, we give an example to illustrate that the generalised Weyl–Titchmarsh m function for the tree operator fails to capture all of its spectral properties.

Item Type:	Book Section
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Differential inequality; regular quantum trees; Hill operator; Weyl–Titchmarsh function
Publisher:	Springer
ISBN:	9783034802628
Related URLs:	Publisher
Last Modified:	19 Oct 2022 08:45
URI:	https://orca.cardiff.ac.uk/id/eprint/18903

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