## 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 2307

The last example above illustrates a problem which will be of great concern to us

in the remainder of this chapter : the problem of finding which formal

The last example above illustrates a problem which will be of great concern to us

in the remainder of this chapter : the problem of finding which formal

**differential****operators**and sets of boundary conditions lead to spectral operators . As our ...Page 2318

Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the

Assistance of William G. Bade and Robert G. ... Let T be the unbounded operator

in Hilbert space defined by the formal

...

Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the

Assistance of William G. Bade and Robert G. ... Let T be the unbounded operator

in Hilbert space defined by the formal

**differential operator**q = - ( d / dx ) 2 and the...

Page 2371

Investigations along the lines initiated by Birkhoff and Tamarkin were continued

by Tamarkin [ 3 ] , who studied a considerably generalized problem for nth order

...

Investigations along the lines initiated by Birkhoff and Tamarkin were continued

by Tamarkin [ 3 ] , who studied a considerably generalized problem for nth order

**differential operators**, by Birkhoff and Langer [ 1 ] , who treated the case of a first...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero