## 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 | 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 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