M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Grubb, G. and Wood, I. G. 2009. M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems. Mathematische Nachrichten 282 (3) , pp. 314-347. 10.1002/mana.200810740

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Abstract

In this paper, we combine results on extensions of operators with recent results on the relation between the M -function and the spectrum, to examine the spectral behaviour of boundary value problems. M -functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the operator to possess spectral points that cannot be detected by the M -function.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	Closed extension; M -function; abstract boundary spaces; boundary triplets; elliptic PDEs; pseudo-differential boundary operators; essential spectrum
Publisher:	Wiley
ISSN:	0025-584X
Last Modified:	18 Oct 2022 13:21
URI:	https://orca.cardiff.ac.uk/id/eprint/13560

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