## 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 2381

If S is some other positive constant and S < € , then ag 2 ag . Let hu ( t ) , ( t , u ) € [

ag , 00 ) * Pi , be the

above . Then , by the uniqueness of the

If S is some other positive constant and S < € , then ag 2 ag . Let hu ( t ) , ( t , u ) € [

ag , 00 ) * Pi , be the

**solution**of equation ( 7 ) which exists in C [ ag , oo ) , by theabove . Then , by the uniqueness of the

**solution**of ( 7 ) , we have hu ( t ) = hult ) ...Page 2391

Appropriate choice of this second

properties of the resolvent as needed below . The following corollary summarizes

the necessary facts in a form convenient for later use . 6 COROLLARY . Let Aa )

and u ...

Appropriate choice of this second

**solution**will enable us to calculate finerproperties of the resolvent as needed below . The following corollary summarizes

the necessary facts in a form convenient for later use . 6 COROLLARY . Let Aa )

and u ...

Page 2394

there exists a

for all sufficiently small u e P + , such that oz and os are continuous in t and Me ...

**solutions**ởi = 0 ( t , - u ( a ) ) and ( i = 0 ; lt , ula ) ) of the equation to = do . ... Thenthere exists a

**solution**oz ( t , u ) of the equation to = u o , defined for 0 St < oo andfor all sufficiently small u e P + , such that oz and os are continuous in t and Me ...

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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