Spectral Theory and Differential Operators
Spectral Theory and Differential Operators
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DOI：
10.1093/oso/9780198812050.001.0001
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发表时间：
2018-09
期刊：
影响因子：
--
通讯作者：
D. Edmunds;Des Evans
中科院分区：
文献类型：
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作者：
D. Edmunds;Des Evans
本书介绍了作用于Banach或Hilbert空间中的封闭线性算子分析中与涉及微分算子的谱问题相关的部分，并应用于此类问题。在前四章对抽象理论进行了阐述之后，本文介绍了Sobolev空间，并建立了Sobolev空间的主要性质。剩下的七章主要是关于二阶椭圆微分算子和相关的边值问题。特别注意的是薛定谔算子的频谱。它的原始形式包含了持久重要性的材料，自1987年该书首次出版以来，这些材料相对不受理论进步的影响。目前的版本不同于旧凭借的纠正轻微错误和改进的各种证明。此外，它在大多数章节的末尾都有注释，目的是让读者对最近的事态发展有一些了解，并有额外的参考资料，使读者能够查阅更详细的叙述。
This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and makes applications to such questions. After the exposition of the abstract theory in the first four chapters, Sobolev spaces are introduced and their main properties established. The remaining seven chapters are largely concerned with second-order elliptic differential operators and related boundary-value problems. Particular attention is paid to the spectrum of the Schrödinger operator. Its original form contains material of lasting importance that is relatively unaffected by advances in the theory since 1987, when the book was first published. The present edition differs from the old by virtue of the correction of minor errors and improvements of various proofs. In addition, it contains Notes at the ends of most chapters, intended to give the reader some idea of recent developments together with additional references that enable more detailed accounts to be accessed.