## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 1915

... the quantum mechanical version of the three body problem , and other contemporary problems of mathematical physics to which the results of Chapter XX

... the quantum mechanical version of the three body problem , and other contemporary problems of mathematical physics to which the results of Chapter XX

**apply**, has a direct short path to these problems ; namely , Theorem XVI.5.19 ...Page 2434

**Applying**Theorem 8 and Corollary 9 , the present theorem follows at once . Q.E.D. By using appropriate “ diagonalizing " transformations ( cf. Theorem XII.3.16 ) , we may**apply**Theorem 21 to analyze a variety of operators .Page 2448

... The perturbation - theoretic methods developed in the preceding section can be adapted for

... The perturbation - theoretic methods developed in the preceding section can be adapted for

**application**to operators with discrete spectrum , and even for**application**to operators with mixed discrete and continuous spectrum .### What people are saying - Write a review

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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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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