The pseudospectrum of an operator with Bessel-type singularities

Boulton, Lyonell and Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046 2024. The pseudospectrum of an operator with Bessel-type singularities. Journal of Spectral Theory 14 (2) , pp. 557-595. 10.4171/JST/505

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Abstract

In this paper, we examine the asymptotic structure of the pseudospectrum of the singular Sturm–Liouville operator L=∂ x ​ (f∂ x ​ )+∂ x ​ subject to periodic boundary conditions on a symmetric interval, where the coefficient f is a regular odd function that has only a simple zero at the origin. The operator L is closely related to a remarkable model examined by Davies in 2007, which exhibits surprising spectral properties balancing symmetries and strong non-self-adjointness. In our main result, we derive a concrete construction of classical pseudo-modes for L and give explicit exponential bounds of growth for the resolvent norm in rays away from the spectrum.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	EMS Press
ISSN:	1664-039X
Date of First Compliant Deposit:	19 April 2024
Date of Acceptance:	15 April 2024
Last Modified:	09 Nov 2024 13:15
URI:	https://orca.cardiff.ac.uk/id/eprint/168182

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