## Linear Operators: Spectral theory |

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Page 968

The group Ř is called the character group or the dual group of R . We topologize

Ř by taking the sets N ( h , K , € ) = { hy e R | | h1 ( x ) — h ( x ) < E , XEK } , as a

base for its topology , where ε > 0 is

...

The group Ř is called the character group or the dual group of R . We topologize

Ř by taking the sets N ( h , K , € ) = { hy e R | | h1 ( x ) — h ( x ) < E , XEK } , as a

base for its topology , where ε > 0 is

**arbitrary**and K is an**arbitrary**compact subset...

Page 1179

Theorem 25 remains valid in the full range 1 < p < oo , and for functions f with

values in an

with trivial modifications of its proof to functions with values in an

...

Theorem 25 remains valid in the full range 1 < p < oo , and for functions f with

values in an

**arbitrary**Hilbert space . PROOF . Note that Theorem 20 goes overwith trivial modifications of its proof to functions with values in an

**arbitrary**Hilbert...

Page 1795

Über eineindeutige , stetige Transformationen von Flächen in sich . Math . Ann .

69 , 176 - 180 ( 1910 ) . Browder , F . E . 1 . The Dirichlet problem for linear elliptic

equations of

Über eineindeutige , stetige Transformationen von Flächen in sich . Math . Ann .

69 , 176 - 180 ( 1910 ) . Browder , F . E . 1 . The Dirichlet problem for linear elliptic

equations of

**arbitrary**even order with variable coefficients . Proc . Nat . Acad .### What people are saying - Write a review

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### 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