## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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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

methods .

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**- theoreticmethods .

Page 2510

Various of the

in the present chapter are developed systematically by T. Kato in his treatise [ 13 ]

. This treatise also contains an extensive bibliography of

Various of the

**perturbation**- theoretic ideas touched on explicitly or by indirectionin the present chapter are developed systematically by T. Kato in his treatise [ 13 ]

. This treatise also contains an extensive bibliography of

**perturbation**theory .Page 2530

Amer . Math . Soc . , Providence , R. I. , 1965 . 18. Spectral

phenomena .

Wiley , New ...

**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 ,Wiley , New ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

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 defined Definition denote dense determined differential operator discrete 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