## Linear Operators: Spectral theory |

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Page 878

of B * ( x ) onto C ( o ( x ) ) has the property that a

- 1 ( u ) ) = ll , € ( x ) . Clearly the requirement that x and g ( u ) = u be

thus led to the ...

of B * ( x ) onto C ( o ( x ) ) has the property that a

**corresponds**to the function x ( x- 1 ( u ) ) = ll , € ( x ) . Clearly the requirement that x and g ( u ) = u be

**corresponding**elements determines the * -isomorphism uniquely and we arethus led to the ...

Page 942

... i.e. , every translate g of an eigenfunction y

eigenfunction

function . Hence N is ...

... i.e. , every translate g of an eigenfunction y

**corresponding**to 2 is also aneigenfunction

**corresponding**to A. Thus every eigenfunction of T , which**corresponds**to a non - zero eigenvalue is a finite dimensional continuousfunction . Hence N is ...

Page 1729

It should be evident from this last formula that much as in the

of the space C ( C ) , we may regard any point x = [ X1 , y ] for which 0 < x < 27 as

belonging , in a suitable sense , to the interior of C ; that is , to argue at such a ...

It should be evident from this last formula that much as in the

**corresponding**caseof the space C ( C ) , we may regard any point x = [ X1 , y ] for which 0 < x < 27 as

belonging , in a suitable sense , to the interior of C ; that is , to argue at such a ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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 neighborhood norm obtained partial positive preceding present problem 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