تقرير
The pseudospectrum of an operator with Bessel-type singularities
| العنوان: | The pseudospectrum of an operator with Bessel-type singularities |
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| المؤلفون: | Boulton, Lyonell, Marletta, Marco |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Spectral Theory, Mathematical Physics, Mathematics - Classical Analysis and ODEs |
| الوصف: | In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ 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. Comment: 31 pages, 4 figures and 1 table. Paper dedicated to Professor E. Brian Davies FRS on the occasion of his 80th birthday. Carbon copy of the final version which appears in the Journal of Spectral Theory, https://ems.press/journals/jst/articles/14297856 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.4171/JST/505 |
| URL الوصول: | http://arxiv.org/abs/2310.13611 |
| رقم الأكسشن: | edsarx.2310.13611 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.4171/JST/505 |
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