On the Localization Conditions for the Spectrum of a Non-Self-Adjoint Sturm–Liouville Operator with Slowly Growing Potential

被引：0
作者：
L. G. Valiullina
Kh. K. Ishkin
机构：
[1] Bashkir State University,
来源：
Journal of Mathematical Sciences | 2019年 / 241卷 / 5期
关键词：
non-self-adjoint differential operator; Keldysh theorem; spectral stability; localization of spectrum; 34B24; 47E05;
D O I：
10.1007/s10958-019-04445-0
中图分类号：
学科分类号：
摘要：
We consider the Sturm–Liouville operator T0 on the semi-axis (0,+∞) with the potential eiθq, where 0 < θ < π and q is a real-valued function that may have arbitrarily slow growth at infinity. This operator does not meet any condition of the Keldysh theorem: T0 is non-self-adjoint and its resolvent does not belong to the Neumann–Schatten class [inline-graphic not available: see fulltext] for any p < ∞. We find conditions for q and perturbations of V under which the localization or the asymptotics of its spectrum is preserved.
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页码：556 / 569
页数：13
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