## Linear Operators: Spectral theory |

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Page 1180

( 66 ) sup lự * ( ) | = | x , z + B ; veY and that in consequence Corollary 22 is valid

for functions f ( x , s ) with values in

generalizes , with hardly any change in its proof , to the space of functions f with

values ...

( 66 ) sup lự * ( ) | = | x , z + B ; veY and that in consequence Corollary 22 is valid

for functions f ( x , s ) with values in

**Hilbert space**. Therefore , Corollary 23generalizes , with hardly any change in its proof , to the space of functions f with

values ...

Page 1262

28 Let a self adjoint operator A in a

there exists a

that Ax = PQx , XEH , P denoting the orthogonal projection of H , on H . 29 Let {

Tn } ...

28 Let a self adjoint operator A in a

**Hilbert space**H with OSASI be given . Thenthere exists a

**Hilbert space**H , 2 H , and an orthogonal projection Q in H , suchthat Ax = PQx , XEH , P denoting the orthogonal projection of H , on H . 29 Let {

Tn } ...

Page 1773

APPENDIX

numbers , together with a complex function ( : , : ) defined on H xH with the

following properties : ( i ) ( x , x ) = 0 if and only if x = 0 ; ( ii ) ( c , c ) 2 0 , 2 e 0 ; ( iii

) ( x + y ...

APPENDIX

**Hilbert space**is a linear vector space H over the field 0 of complexnumbers , together with a complex function ( : , : ) defined on H xH with the

following properties : ( i ) ( x , x ) = 0 if and only if x = 0 ; ( ii ) ( c , c ) 2 0 , 2 e 0 ; ( iii

) ( x + y ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive 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 differential equations domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem Proc projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero