## Linear Operators: Spectral theory |

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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

and 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 |Jož| < g (**) 2 (Hint: Use Exercise 33and the ...

Page 1275

Jacobi

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

—q| > 1.

Jacobi

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

**matrix**{ak}, j, k > 0, is said to be a Jacobi**matrix**if (i) (l pa (ii) ('pa day. all p, q, 0, p—q| > 1.

Page 1361

It follows from the spectral theorem that there exist

Ao) = UAUT", where U = {uv} 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(Ao) = UAUT", where U = {uv} is a unitary

**matrix**and A is the**matrix**{ai}} = {2,3,4},where A1, ..., A, are the eigenvalues of S(Ao) each repeated according to its ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero