## Linear Operators: Spectral operators |

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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 X 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 8 ( )

defined for S in the half

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

analytic ...

The semi - group S ( t ) has a strongly analytic extension to a semi - group 8 ( )

defined for S 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

analytic ...

Page 2087

... domain ( 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 ( 5 ) defined for in the half

... domain ( 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 ( 5 ) defined for in the half

**plane**R ( S ) ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero