## 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 77

Page 2325

5 and from

16 ) , and

representation m = 1 m = 1 $ * ~ 2mn + & + 22 + Smu - m , and that the zero Šn of

M ...

5 and from

**formulas**( 16 ) and ( 14 ) . It also follows , from Lemma 3 . 5 ,**formula**(16 ) , and

**formula**( 14 ) , that the zero Šr of M ( u ) in Rom has the asymptoticrepresentation m = 1 m = 1 $ * ~ 2mn + & + 22 + Smu - m , and that the zero Šn of

M ...

Page 2334

On the other hand , it follows from the asymptotic

excise from the angle A of the u - plane ( defined by

radius ε ...

On the other hand , it follows from the asymptotic

**formula**( 26 ) and from the**formula**( 21 ) giving the form of the kernel defining the operator Gu that if weexcise from the angle A of the u - plane ( defined by

**formula**( 8 ) ) a circle ofradius ε ...

Page 2340

It follows immediately from

in the form ( 55 ) ( B , Gus ) = - n Tex ( de ) ... Moreover ,

be differentiated any number of times with respect to x , and still remain a valid ...

It follows immediately from

**formulas**( 52 ) and ( 34 ) that ( B , Guf ) can be writtenin the form ( 55 ) ( B , Gus ) = - n Tex ( de ) ... Moreover ,

**formula**( 56 ) may clearlybe differentiated any number of times with respect to x , and still remain a valid ...

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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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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