论通过有间隙算子的自伴延拓产生新的本质谱
On creating new essential spectrum by self-adjoint extension of gapped operators
AI总结：
本文针对无限亏指数的稠定有间隙对称算子，给出一般延拓框架以构造使间隙任意指定部分成为本质谱的自伴延拓，并阐明其简洁的算子论机制。
摘要：
给定一个具有无限亏指数、稠定且有间隙的对称算子，本文展示了如何在一个一般延拓框架内识别并构造这样的自伴延拓：它们允许将间隙中任意指定的部分作为本质谱。通过自伴延拓在间隙中产生新谱是一个历史悠久、近来又获得深刻理解的问题，并且在若干近期应用中仍具有现实意义。尽管在亏指数无限时，间隙内任何类型的谱都可以由适当的自伴延拓产生已是既定事实，但本讨论的优点在于揭示了此类延拓产生过程中清晰而简单的算子论机制。
英文摘要：
Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap as essential spectrum are identified and constructed within a general extension scheme. The emergence of new spectrum in the gap by self-adjoint extension is a problem with a long history and recent deep understanding, and yet it remains topical in several recent applications. Whereas it is already an established fact that, in case of infinite deficiency index, any kind of spectrum inside the gap can be generated by a suitable self-adjoint extension, the present discussion has the virtue of showing the clean and simple operator-theoretic mechanism of emergence of such extensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
