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Spectrum and Resolvent

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

Abstract

The eigenvalues of an n × n matrix M constitute a (finite) point set in the complex plane, called the spectrum of M. If A is any linear operator in a Hilbert space ℌ, the complex plane ℂ is similarly decomposed into two parts: the spectrum of A, denoted by σ(A), and the resolvent set, denoted by ρ(A). The spectrum of A is further decomposed into the point spectrum (A), the continuous spectrum (A), and the residual spectrum Rσ(A).

Keywords

Continuous, point, and residual spectrum eigenvectors and approximate eigenvectors resolvent analyticity of the resolvent the Cayley transform von Neumann’s theory of the extension of symmetric operators the deficiency indices of a symmetric operator second definition of self-adjoint 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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