## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 77

Page 1309

MICHIGAN LIBRARIES boundary

way , in case ( i ) above the operator T , if it is determined by a separated set of

boundary

one ...

MICHIGAN LIBRARIES boundary

**condition**determining T is real . In the sameway , in case ( i ) above the operator T , if it is determined by a separated set of

boundary

**conditions**, is determined by two boundary**conditions**, one at a andone ...

Page 1310

Then the boundary

of ( 1 - 2 ) 9 = 0 square - integrable at a and satisfying the boundary ... In case ( iii

) , one boundary

Then the boundary

**conditions**are real , and there is exactly one solution y ( t , 2 )of ( 1 - 2 ) 9 = 0 square - integrable at a and satisfying the boundary ... In case ( iii

) , one boundary

**condition**is to be imposed , since , according to Theorem XII .Page 1519

We shall consequently not do more than examine a few of the simpler special

cases which arise . First of all , if we impose the

second

boundary ...

We shall consequently not do more than examine a few of the simpler special

cases which arise . First of all , if we impose the

**condition**B ( 1 ) = 0 , and asecond

**condition**at t = + 1 , the unique solution of Lf = af satisfying the givenboundary ...

### 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

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

### Common terms and phrases

additive adjoint operator 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