A discussion of the spectral theorem for self-adjoint operators is presented, including details of the resolution of the identity and functions of self-adjoint operators. Although a complete proof of this theorem for a given operator is not presented, different approaches to the proof are indicated. Spectral measures of some simple examples are discussed. Chapter 9 is devoted to some consequences of the spectral theorem. A denotes the σ-algebra of Borel sets in ℝ.
KeywordsOrthonormal Basis Orthogonal Projection Multiplication Operator Spectral Measure Polar Decomposition
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