## Linear Operators: Spectral operators |

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The Principal Abstract

The Principal Abstract

**Perturbation**Theorem In this section we shall study**perturbations**of an operator whose resolvent is compact . The principal result gives conditions under which such an operator ...Page 2377

In cases where closed - form solutions are not available , physicists have been accustomed to discussing the eigenfunction theory of the partial differential operators which arise in these subject areas using

In cases where closed - form solutions are not available , physicists have been accustomed to discussing the eigenfunction theory of the partial differential operators which arise in these subject areas using

**perturbation**- theoretic ...Page 2530

**Perturbation**of spectra in Hilbert space . Lectures in Applied Math . , Vol . III , Amer . Math . Soc . , Providence , R. I. , 1965 . 18. Spectral**perturbation**phenomena .**Perturbation**Theory and its Applications in Quantum Mechanics ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero