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On the HELP Inequality for Hill Operators on Trees

Brown, Brian Malcolm and Schmidt, Karl Michael 2012. On the HELP Inequality for Hill Operators on Trees. In: 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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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
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Last Modified: 06 Mar 2018 21:03

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