The pseudospectrum of an operator with Bessel-type singularities

Lyonell Boulton, Marco Marletta

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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
Publication statusE-pub ahead of print - 31 May 2024


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


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