## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 53

Page 1629

CHAPTER XIV Linear

The Cauchy Problem , Local Dependence In this chapter , we shall discuss a

variety of theorems having to do with linear

the ...

CHAPTER XIV Linear

**Partial**Differential Equations and Operators 1 . IntroductionThe Cauchy Problem , Local Dependence In this chapter , we shall discuss a

variety of theorems having to do with linear

**partial**differential operators . Sincethe ...

Page 1633

A third category of formal

the operator 22 Ox , Ox ? This sort of operator is closely related to the theory of

semi - groups , where we have already seen general equations of the form = AT ...

A third category of formal

**partial**differential operators is the parabolic , typified bythe operator 22 Ox , Ox ? This sort of operator is closely related to the theory of

semi - groups , where we have already seen general equations of the form = AT ...

Page 1703

The Elliptic Boundary Value Problem Can the boundary value theory and the

spectral theory of Chapter XIII be generalized to

the present section it will be seen that it can , at least for the class of elliptic

...

The Elliptic Boundary Value Problem Can the boundary value theory and the

spectral theory of Chapter XIII be generalized to

**partial**differential operators ? Inthe present section it will be seen that it can , at least for the class of elliptic

**partial**...

### 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