## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 35

Page 916

The sets e, will be called the

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

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

The sets e, will be called the

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

**multiplicity**k.If u(e) > 0 for all k, the representation is said to have infinite

**multiplicity**.Page 1091

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

according to its

eigenvalues of Ta, with repetitions according to

2 ...

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

according to its

**multiplicity**. Then there exist enumerations A, (T,) of the non-zeroeigenvalues of Ta, with repetitions according to

**multiplicity**, such that lim A, (T,) =2 ...

Page 1217

The sets e, will be called the

> 0 and u(erri) = 0 then the ordered representation is said to have

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

The sets e, will be called the

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

**multiplicity**k. Ifu(es) > 0 for all k, the representation is said to have infinite

**multiplicity**.### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero