## 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 1930

If Eis a Boolean algebra of subsets of the complex

set and the whole

a spectral measure E on & is called a resolution of the identity ( or a spectral ...

If Eis a Boolean algebra of subsets of the complex

**plane**which contains the voidset and the whole

**plane**, in short , if & is a field of sets in the complex**plane**, thena spectral measure E on & is called a resolution of the identity ( or a spectral ...

Page 2043

The semi - group S ( t ) has a strongly analytic extension to a semi - group S ( 5 )

defined for % in the half

problem presented by the equations ( ii ) , ( iii ) , ( iv ) is analytic in t and has an ...

The semi - group S ( t ) has a strongly analytic extension to a semi - group S ( 5 )

defined for % in the half

**plane**R ( S ) > 0 . The unique solution to the Cauchyproblem presented by the equations ( ii ) , ( iii ) , ( iv ) is analytic in t and has an ...

Page 2087

... ( p ) T ( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi -

group s ( t ) , t 20 , of bounded linear operators in HP and S ( t ) has a strongly

analytic extension to a semi - group S ( ) defined for & in the half

.

... ( p ) T ( 29 ) ( RN ) is the infinitesimal generator of a strongly continuous semi -

group s ( t ) , t 20 , of bounded linear operators in HP and S ( t ) has a strongly

analytic extension to a semi - group S ( ) defined for & in the half

**plane**R ( S ) > 0.

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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