数学证明
计算机科学
可见的
研究生
牙石(牙科)
量子场论
真实分析
域代数上的
领域(数学)
数学
纯数学
离散数学
物理
量子力学
数学物理
医学
牙科
教育学
心理学
几何学
标识
DOI:10.1017/9781009232487
摘要
This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.
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