## 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

tita - fati identically

number of

d ] ...

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

tita - fati identically

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

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

Page 1474

Since , by Lemma 35 , o ( t , 2 ) has a

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

% of ost , 21 ) contains a

Since , by Lemma 35 , o ( t , 2 ) has a

**zero**between every pair of**zeros**of ost , 27) , we have only to show that the interval ( a , z ] between a and the smallest

**zero**% of ost , 21 ) contains a

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

If we can show that o ( : , 22 ) has a

have established that o ( : , 2 , ) has at least n + 1

the fact that he is in Jn . It is sufficient to prove that o ( : , 22 ) has a

...

If we can show that o ( : , 22 ) has a

**zero**in ( a , z ; ] and a**zero**in [ Zg , b ) , we willhave established that o ( : , 2 , ) has at least n + 1

**zeros**in ( a , b ) , contradictingthe fact that he is in Jn . It is sufficient to prove that o ( : , 22 ) has a

**zero**in ( a , zı ]...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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