The pseudospectrum of an operator with Bessel-type singularities
Lyonell Boulton
Heriot-Watt University, Edinburgh, UKMarco Marletta
Cardiff University, Cardiff, UK
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Abstract
In this paper, we examine the asymptotic structure of the pseudospectrum of the singular Sturm–Liouville operator subject to periodic boundary conditions on a symmetric interval, where the coefficient is a regular odd function that has only a simple zero at the origin. The operator 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 and give explicit exponential bounds of growth for the resolvent norm in rays away from the spectrum.
Cite this article
Lyonell Boulton, Marco Marletta, The pseudospectrum of an operator with Bessel-type singularities. J. Spectr. Theory 14 (2024), no. 2, pp. 557–595
DOI 10.4171/JST/505