Math 713 Fall 2006 Lecture Notes on Functional Analysis
نویسنده
چکیده
1. Topological Vector Spaces 1 2. Banach Algebras 10 2.1. ∗–Algebras (over complexes) 15 2.2. Exercises 18 3. The Spectral Theorem 19 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 24 3.2. Integration with respect to a Projection Valued Measure 25 3.3. The Functional Calculus 32 4. Unbounded Operators 35 4.1. Closed, symmetric and self-adjoint operators 35 4.2. Differential operators 39 4.3. The Laplacian over R 41 4.4. The Laplacian in one dimension 43 4.5. A non-self-adjoint version of the Laplacian 44 4.6. von Neumann’s criteria for self-adjointness 46 4.7. The spectral theorem for unbounded self-adjoint operators 49 5. Compact Operators 53 5.1. Riesz Theory of Compact Operators 55 6. Semigroups of Operators 60
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