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Spectral Decomposition of Self-Adjoint and Unitary Operators

  • Robert D. Richtmyer
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

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.

Keywords

Applications 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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Copyright information

© Springer-Verlag New York Inc. 1978

Authors and Affiliations

  • Robert D. Richtmyer
    • 1
  1. 1.Department of Physics and AstrophysicsUniversity of ColoradoBoulderUSA

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