## Linear Operators: Spectral theory |

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Page 916

The sets en will be called the

ek ) > 0 and u ( ek + 1 ) = 0 then the ordered representation is said to have

The sets en will be called the

**multiplicity**sets of the ordered representation . If u (ek ) > 0 and u ( ek + 1 ) = 0 then the ordered representation is said to have

**multiplicity**k . If ulex ) > 0 for all k , the representation is said to have infinite**multiplicity**...Page 1091

Let im ( T ) be an enumeration of the non - zero eigenvalues of T , each repeated

according to its

zero eigenvalues of Tn , with repetitions according to

...

Let im ( T ) be an enumeration of the non - zero eigenvalues of T , each repeated

according to its

**multiplicity**. Then there exist enumerations am ( Tn ) of the non -zero eigenvalues of Tn , with repetitions according to

**multiplicity**, such that m 2 1...

Page 1217

If u ( ex ) > 0 for all k , the representation is said to have infinite

ordered representations U and U of H relative to T and I respectively , with

measures u and ű , and

if u ū ...

If u ( ex ) > 0 for all k , the representation is said to have infinite

**multiplicity**. Twoordered representations U and U of H relative to T and I respectively , with

measures u and ű , and

**multiplicity**sets { en } and { ēn } will be called equivalentif u ū ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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