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- Title
The pseudospectrum of an operator with Bessel-type singularities.
- Authors
Boulton, Lyonell; Marietta, Marco
- 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.
- Subjects
PSEUDOSPECTRUM; CONCRETE construction; DIFFERENTIAL operators; MULTIFRACTALS
- Publication
Journal of Spectral Theory, 2024, Vol 14, Issue 2, p557
- ISSN
1664-039X
- Publication type
Article
- DOI
10.4171/JST/505