## 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 78

Page 1976

JEB SES Then for every bounded Borel scalar function y defined on the spectrum

o ( A ) , the

E - measurable function of s . The

JEB SES Then for every bounded Borel scalar function y defined on the spectrum

o ( A ) , the

**integral**( ii ) o ( a ) E ( d ) ; Â ( s ) ) O ( A ) is an e - essentially boundedE - measurable function of s . The

**integral**( iii ) Elo ; Â ( s ) ) e ( ds ) , 0EB , is a ...Page 1990

Here , we shall first be concerned with certain special examples of convolutions

which map H into H , which belong to the algebra A , and which have an

representation in one of the two forms ( 18 ) ( f * Q ) ( p ( s – t ) f ( t ) dt , QEH , RN

...

Here , we shall first be concerned with certain special examples of convolutions

which map H into H , which belong to the algebra A , and which have an

**integral**representation in one of the two forms ( 18 ) ( f * Q ) ( p ( s – t ) f ( t ) dt , QEH , RN

...

Page 2405

If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the

) | h ( ) u ( dt ) ( 14 ) exists for u - almost all s , and that , writing fl . for the norm of

an element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...

If he L ; ( S , E , p ) and 2 sr < 00 , it follows that the

**integral**( Ah ) ( 8 ) = S 14 ( 8 , t) | h ( ) u ( dt ) ( 14 ) exists for u - almost all s , and that , writing fl . for the norm of

an element f of L ( S , E , u ) , we have Ahl , $ { A } , \ h \ , . Thus , using Theorem ...

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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