## 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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Results 1-3 of 53

Page 2020

We may therefore conclude from Theorem 7 that the natural closed extension As

of the

whole complex plane unless A is of order zero , that is , none of its elements ...

We may therefore conclude from Theorem 7 that the natural closed extension As

of the

**formal**differential operator ( 18 ) with An P = 0 has its spectrum o ( As ) thewhole complex plane unless A is of order zero , that is , none of its elements ...

Page 2307

Let – be a

interval I . Let the deficiency indices of both be equal to an integer m . Let Aį , i = 1

, . . . , m , be a set of m linearly independent boundary values for 7 . Let S be ...

Let – be a

**formally**symmetric**formal**differential operator of order n defined on aninterval I . Let the deficiency indices of both be equal to an integer m . Let Aį , i = 1

, . . . , m , be a set of m linearly independent boundary values for 7 . Let S be ...

Page 2371

... who studied the case in which linear conditions are imposed at interior points

of the interval of definition of a

theoretic approach via perturbation theorems used in Section 2 was introduced ...

... who studied the case in which linear conditions are imposed at interior points

of the interval of definition of a

**formal**differential operator . The abstract operator -theoretic approach via perturbation theorems used in Section 2 was introduced ...

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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 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