Spectral Theory of Operators
Spectral measures, functional calculus, and unbounded operators.
Spectral Theory of Operators. Spectral measures, functional calculus, and unbounded operators.
Foundations and canonical references
The standard treatments of spectral theory of operators approach the subject from complementary angles. Reed, Methods of Modern Mathematical Physics I: Functional Analysis (1980) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Kato, Perturbation Theory for Linear Operators (1995) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for spectral theory of operators include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1980Methods of Modern Mathematical Physics I: Functional Analysisreed-1980, simon-1980
- textbook · primary · 1995Perturbation Theory for Linear Operatorskato-1995
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