## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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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

... of bounded linear operators in HP and S ( t ) has a strongly analytic extension

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

HP there is one and only one continuous mapt → olt ) of [ 0 , 00 ) into HP which ...

... 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 . For every gro ) inHP there is one and only one continuous mapt → olt ) of [ 0 , 00 ) into HP which ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

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