## Linear Operators: Spectral theory |

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Page 1343

Thus E ( M ( 2 ) ; U ) is non - zero for a near do , a € Oo , and it follows that for a

number of distinct points in the spectrum of M ( a ) , the sets { 2 € o ln ( ) Z s } are ...

Thus E ( M ( 2 ) ; U ) is non - zero for a near do , a € Oo , and it follows that for a

**sufficiently**close to 20 , o ( M ( 2 ) ) U is non - void . Thus if n ( a ) denotes thenumber of distinct points in the spectrum of M ( a ) , the sets { 2 € o ln ( ) Z s } are ...

Page 1450

q ' ( t ) ( g ( t ) ' ) 2 $ .04 1 602 ) - dt • đo 19 ( t ) / 3 / 2 19 ( t ) | 5/2 for

small bo , and if S * ig ( e ) - de < 60 for

d ) If qlt ) → 00 as t → 0 , g ( t ) is monotone decreasing for

q ' ( t ) ( g ( t ) ' ) 2 $ .04 1 602 ) - dt • đo 19 ( t ) / 3 / 2 19 ( t ) | 5/2 for

**sufficiently**small bo , and if S * ig ( e ) - de < 60 for

**sufficiently**small bo , then o ( t ) is void . (d ) If qlt ) → 00 as t → 0 , g ( t ) is monotone decreasing for

**sufficiently**small t , S.Page 1760

... D ( W ) , ( SJ ) ( x ) = ( W1 ) ( x ; 2 ) for æ in C. Then , by ( vi ) , Sk is bounded

and of norm at most Mz . We shall show that ( vii ) for each k 20 , and for each

C ) .

... D ( W ) , ( SJ ) ( x ) = ( W1 ) ( x ; 2 ) for æ in C. Then , by ( vi ) , Sk is bounded

and of norm at most Mz . We shall show that ( vii ) for each k 20 , and for each

**sufficiently**small positive a Sa ( k ) , the mapping 1- « S has a range dense in Ê ! (C ) .

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### Common terms and phrases

additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero