Abstract

Non-self adjoint operators describe problems in science and engineering that lack symmetry and unitarity. They have applications in convection–diffusion processes, quantum mechanics, fluid mechanics, optics, wave-guide theory, and other fields of physics. This paper reviews some important aspects of the eigenvalue problems of non-self-adjoint differential operators and discusses the spectral properties of various non-self-adjoint differential operators. Their eigenvalues can be computed for ground and perturbed states by their spectra and pseudospectra. This work also discusses the contemporary results on the finite number of eigenvalues of non-self-adjoint operators and the implications it brings in modeling physical problems.

中文翻译：

---

非自伴算子特征值问题入门

摘要

非自伴随算子描述了科学和工程中缺乏对称性和幺正性的问题。它们在对流扩散过程、量子力学、流体力学、光学、波导理论和其他物理领域都有应用。本文回顾了非自伴微分算子特征值问题的一些重要方面，并讨论了各种非自伴微分算子的谱性质。可以通过它们的光谱和伪光谱计算它们的基态和扰动态的特征值。这项工作还讨论了非自伴算子的有限数量特征值的当代结果及其在物理问题建模中带来的影响。