## 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 - fat , identically

only a finite number of

) ...

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

tita - fat , identically

**zero**in [ c , d ] . Thus ( total ) ... Moreover , since f1 and fí haveonly a finite number of

**zeros**in [ c , d ] , we must have pi ( t ) = po ( t ) , 9. ( t ) = 9 ( t) ...

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 o ( t , 2 , ) contains a

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

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

**zero**zof o ( t , 2 , ) contains a

**zero**of o ( t , 2 ) , and we will have established that o ( t ...Page 1475

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

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

fact that he is in J It is sufficient to prove that o ( : , 12 ) has a

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

**zero**in ( a , z7 ] and a**zero**in [ zą , b ) , we willhave established that o ( :, ) has at least n + 1

**zeros**in ( a , b ) , contradicting thefact that he is in J It is sufficient to prove that o ( : , 12 ) has a

**zero**in ( a , z7 ] , for ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### Common terms and phrases

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