## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 89

Page 1463

is an evident consequence of

the pair of functions sin At and sin ut for u > A; the corollary by the pair of

functions ...

**Statement**(a) is the special case ti = 12 of the preceding theorem.**Statement**(b)is an evident consequence of

**statement**(a). Q.E.D. The theorem is illustrated bythe pair of functions sin At and sin ut for u > A; the corollary by the pair of

functions ...

Page 1469

The operator r is bounded below if and only if it is finite below A for some finite A.

Thus

) ...

The operator r is bounded below if and only if it is finite below A for some finite A.

Thus

**statement**(a) follows immediately from the preceding lemma. To prove**statement**(b), note that t is finite below Żo, but not below any A - Wo.**Statement**(b) ...

Page 1771

8*T*(X)u(t, w) = 0, t > 0, a e2, and such that in us.')-10-0. PRoof.

follows from the preceding theorem and Theorem 6.23.

...

8*T*(X)u(t, w) = 0, t > 0, a e2, and such that in us.')-10-0. PRoof.

**Statement**(i)follows from the preceding theorem and Theorem 6.23.

**Statement**(ii) follows from**statement**(ii) of the preceding theorem, since a function satisfying the hypotheses...

### 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

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

### 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