The pseudospectrum of an operator with Bessel-type singularities

Lyonell Boulton, Marco Marletta

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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.
Original languageEnglish
JournalJournal of Spectral Theory
Early online date31 May 2024
DOIs
Publication statusE-pub ahead of print - 31 May 2024

Keywords

  • spectrum and pseudospectrum
  • ordinary differential operators
  • pseudo-modes

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