## Linear Operators: Spectral theory |

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Page 1002

5 A

periodic if for each e > 0 there exists a ... Show that every such almost periodic

function may be approximated uniformly by linear combinations of functions of

the form ...

5 A

**continuous function**f of two real variables x = ( x1 , x2 ) is called almostperiodic if for each e > 0 there exists a ... Show that every such almost periodic

function may be approximated uniformly by linear combinations of functions of

the form ...

Page 1899

A Abel summability , of series , II.4.42 ( 76 ) Abelian group , ( 34 ) Absolutely

set function and Set function ) space of , additional properties , IV.15 ( 378 )

definition ...

A Abel summability , of series , II.4.42 ( 76 ) Abelian group , ( 34 ) Absolutely

**continuous functions**, definition , IV.2.22 ( 242 ) set function . ( See Continuousset function and Set function ) space of , additional properties , IV.15 ( 378 )

definition ...

Page 1903

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. on non -

existence in Ln , 0 < p < 1 , V.7.37 ( 438 )

Absolutely

definition ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. on non -

existence in Ln , 0 < p < 1 , V.7.37 ( 438 )

**Continuous functions**. ( See alsoAbsolutely

**continuous functions**) as a B - space , additional properties , IV.15definition ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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 singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero