## Linear Operators: Spectral theory |

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Page 1463

Since all the terms in the integral on the right are non - negative , we must have

tite - fatı identically

number of

...

Since all the terms in the integral on the right are non - negative , we must have

tite - fatı identically

**zero**in [ c , d ] . ... Moreover , since fı and fí have only a finitenumber of

**zeros**in [ c , d ] , we must have Pi ( t ) = P2 ( t ) , 9. ( t ) = 92 ( t ) for te [ c...

Page 1474

Since , by Lemma 35 , ost , a ) has a

) , we have only to show that the interval ( a , z ] between a and the smallest

z of o ( t , 2 , ) contains a

Since , by Lemma 35 , ost , a ) has a

**zero**between every pair of**zeros**of o ( t , 22) , we have only to show that the interval ( a , z ] between a and the smallest

**zero**z of o ( t , 2 , ) contains a

**zero**of ost , a ) , and we will have established that o ( t ...Page 1475

If we can show that o ( :, ) has a

have established that o ( :, 22 ) has at least n + 1

the fact that n , is in Jn . It is sufficient to prove that o ( :, 12 ) has a

...

If we can show that o ( :, ) has a

**zero**in ( a , zz ) and a**zero**in [ 22 , b ) , we willhave established that o ( :, 22 ) has at least n + 1

**zeros**in ( a , b ) , contradictingthe fact that n , is in Jn . It is sufficient to prove that o ( :, 12 ) has a

**zero**in ( a , 21 )...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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