## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 88

Page 1080

34 (Bendixon) Let A be as in Exercise 25, and suppose also that the

elements of A are real. Let C = (A–A*), and let g be the maximum of the absolute

values of the

the ...

34 (Bendixon) Let A be as in Exercise 25, and suppose also that the

**matrix**elements of A are real. Let C = (A–A*), and let g be the maximum of the absolute

values of the

**matrix**elements of C. Then |Joã sg (**) 2 (Hint: Use Exercise 33 andthe ...

Page 1275

Jacobi

problem made in Section 8 can be carried considerably ... An infinite

, k > 0, is said to be a Jacobi

Jacobi

**Matrices**and the Moment Problem The investigations of the momentproblem made in Section 8 can be carried considerably ... An infinite

**matrix**{an}, j, k > 0, is said to be a Jacobi

**matrix**if (i) ava - dor, all p, q, (ii) apa = 0, p—q| > 1.Page 1361

It follows from the spectral theorem that there exist

20) = UAU-", where U = {ug) is a unitary

where A1, ..., A, are the eigenvalues of S(Ao) each repeated according to its ...

It follows from the spectral theorem that there exist

**matrices**U and A such that S(20) = UAU-", where U = {ug) is a unitary

**matrix**and A is the**matrix**{au} = {A,öu},where A1, ..., A, are the eigenvalues of S(Ao) each repeated according to its ...

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

38 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix 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