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

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Results 1-3 of 69

Page 2017

and the fraction in the

s2 ) * + 16s1 sf } 1 / 2 which is bounded on all of R " . Thus As has a resolution of

the identity . Furthermore , the set S , is the null set { 8 | 81 = 82 = 0 } , so that Ag ...

and the fraction in the

**inequality**( i ) of Theorem 6 is 1si - sl ? + 2 | 818212 { ( si -s2 ) * + 16s1 sf } 1 / 2 which is bounded on all of R " . Thus As has a resolution of

the identity . Furthermore , the set S , is the null set { 8 | 81 = 82 = 0 } , so that Ag ...

Page 2190

Thus for some constant K we have | S ( ) < K \ f | and to prove the final

of the present theorem it will suffice to prove that fe = S ( $ ) . Since both terms in

this

Thus for some constant K we have | S ( ) < K \ f | and to prove the final

**inequality**of the present theorem it will suffice to prove that fe = S ( $ ) . Since both terms in

this

**inequality**are continuous functions of f , it will suffice to prove it for every ...Page 2399

By ( 44 ) and Hölder ' s

} " sko { f * 14 1 / 2 L112 | S | 2 . The

43 ) and ( 45 ) . Since the

By ( 44 ) and Hölder ' s

**inequality**we have ( 45 ) { { * ( ( ve ) – ( 0 + 3 ) ( x ) ] 2 due} " sko { f * 14 1 / 2 L112 | S | 2 . The

**inequality**( 42a ) follows immediately from (43 ) and ( 45 ) . Since the

**inequality**( 42b ) may be deduced in a precisely ...### What people are saying - Write a review

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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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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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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