## Linear Operators: Spectral theory |

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Page 1033

It follows immediately that g has the Laurent expansion с g ( a ) = ah + b + ; + . . .

in the neighborhood of 2 = 0 . Consequently , the

it ...

It follows immediately that g has the Laurent expansion с g ( a ) = ah + b + ; + . . .

in the neighborhood of 2 = 0 . Consequently , the

**analytic**function g ( a ) - ał is**analytic**for all finite and infinite 1 and vanishes at a = 0 . By Liouville ' s theorem ,it ...

Page 1040

y ( 2 ) is

R ( Q ; T ) * y vanishes which will prove that y ( a ) is

ām , so that y ( a ) can only fail to be

y ( 2 ) is

**analytic**even at a = rm . It will now be shown that yề ( 2 ) = 2N Eām ; T ) *R ( Q ; T ) * y vanishes which will prove that y ( a ) is

**analytic**at all the points à =ām , so that y ( a ) can only fail to be

**analytic**at the point à = 0 . To show this ...Page 1102

The determinant det ( I + zTn ) is an

z , if Tn operates in finite - dimensional space , and hence more generally if Tn

has a finite - dimensional range . Thus , since a bounded convergent sequence

of ...

The determinant det ( I + zTn ) is an

**analytic**( and even a polynomial ) function ofz , if Tn operates in finite - dimensional space , and hence more generally if Tn

has a finite - dimensional range . Thus , since a bounded convergent sequence

of ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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