Spectral Decomposition of Self-Adjoint and Unitary Operators
The main subject of this chapter is the analogue, for a self-adjoint operator in a Hilbert Space, of the problem of diagonalizing a Hermitian matrix and thereby expressing the matrix in terms of its eigenvalues and eigenvectors.
KeywordsApplications of complex variable methods to matrix theory projectors resolution of the identity canonical form of a matrix Jordan form nilpotent part of a matrix; generalized eigenvector and eigenspace Schur’s theorem on triangularization functions and distributions as boundary values of analytic functions the Laplace transform canonical representation of self-adjoint and unitary operators weak, strong, and uniform convergence of bounded operators spectrum of A as the t-set on which Et is not constant functions of operators bounded observables the polar decomposition of an operator
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