## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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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

Then 1.l < 1.. Since, by Lemma 35. a(t, 1.) has a

of a(t, 1.1), we have only to show that the interval (a, z] between a and the

smallest

that a(t ...

Then 1.l < 1.. Since, by Lemma 35. a(t, 1.) has a

**zero**between every pair of**zeros**of a(t, 1.1), we have only to show that the interval (a, z] between a and the

smallest

**zero**z of a(t, /ll) contains a**zero**of a(t, 1.), and we will have establishedthat a(t ...

Page 1475

If we can show that a(-, 1,) has a

established that a(-, 1,) has at least n+1

1, is in J". It is sufficient to prove that o(-, 1,) has a

If we can show that a(-, 1,) has a

**zero**in (a, zl] and a**zero**in [z,, b), we will haveestablished that a(-, 1,) has at least n+1

**zeros**in (a, b), contradicting the fact that1, is in J". It is sufficient to prove that o(-, 1,) has a

**zero**in (a, 21], for then it will ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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