## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 76

Page 1301

They are clearly linearly

it would follow that has a boundary value at a which is

. . . , An - 1 , and hence has at least n + 1

They are clearly linearly

**independent**. If the assertion of the corollary were false ,it would follow that has a boundary value at a which is

**independent**of the set A , ,. . . , An - 1 , and hence has at least n + 1

**independent**boundary values at a .Page 1306

The following table gives the number of linearly

0 = 0 square integrable at a or b when I ( a ) + 0 . There are four possibilities as

shown by the discussion above . Number of linearly

The following table gives the number of linearly

**independent**solutions of ( 1 – 2 )0 = 0 square integrable at a or b when I ( a ) + 0 . There are four possibilities as

shown by the discussion above . Number of linearly

**independent**solutions ...Page 1311

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. with end

points a , b . The operator T = T ( T ) will be an operator obtained from t by the

imposition of a set , which may be vacuous , of k linearly

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. with end

points a , b . The operator T = T ( T ) will be an operator obtained from t by the

imposition of a set , which may be vacuous , of k linearly

**independent**boundary ...### What people are saying - Write a review

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

### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 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 Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero