The pseudospectrum of an operator with Bessel-type singularities
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914832974872576 |
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| author | Boulton, Lyonell Marletta, Marco |
| author_facet | Boulton, Lyonell Marletta, Marco |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_13611 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The pseudospectrum of an operator with Bessel-type singularities Boulton, Lyonell Marletta, Marco Spectral Theory Mathematical Physics Classical Analysis and ODEs 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. |
| title | The pseudospectrum of an operator with Bessel-type singularities |
| topic | Spectral Theory Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2310.13611 |