## Linear Operators: Spectral theory |

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Page 878

In the notation of the preceding proof the * - isomorphism y H + y ( x - 1 ( - ) ) of B *

( x ) onto Clo ( x ) ) has the property that x

) = u , u ( x ) . Clearly the requirement that x and g ( u ) = u be

In the notation of the preceding proof the * - isomorphism y H + y ( x - 1 ( - ) ) of B *

( x ) onto Clo ( x ) ) has the property that x

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

**corresponding**...Page 942

Thus every eigenfunction of T , which

finite dimensional continuous function . Hence N is orthogonal to every

eigenfunction of T , except to those

Theorem X . 3 .

Thus every eigenfunction of T , which

**corresponds**to a non - zero eigenvalue is afinite dimensional continuous function . Hence N is orthogonal to every

eigenfunction of T , except to those

**corresponding**to 2 = 0 . It follows fromTheorem X . 3 .

Page 1729

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

of the space 0 % ( 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 0 % ( 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

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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