## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 83

Page 1900

Almost periodic functions ,

properties , IV . 15 ( 879 )

– 387 ) study of , IV . 7 Almost uniform ( or u - uniform convergence )

. 6 .

Almost periodic functions ,

**definition**, IV . 2 . 25 ( 242 ) space of , additionalproperties , IV . 15 ( 879 )

**definition**, IV . 2 . 25 ( 242 ) remarks concerning , ( 386– 387 ) study of , IV . 7 Almost uniform ( or u - uniform convergence )

**definition**, III. 6 .

Page 1907

Nelson Dunford, Jacob T. Schwartz. Egoroff theorem , on almost everywhere and

u - uniform convergence , III . 6 . 12 ( 149 ) Eigenvalue ,

) , VII . 11 ( 606 ) , X . 3 . 1 ( 902 ) Eigenvector ,

Nelson Dunford, Jacob T. Schwartz. Egoroff theorem , on almost everywhere and

u - uniform convergence , III . 6 . 12 ( 149 ) Eigenvalue ,

**definition**, VII . 1 . 2 ( 556) , VII . 11 ( 606 ) , X . 3 . 1 ( 902 ) Eigenvector ,

**definition**, VII . 1 . 2 ( 556 ) , X . 3 ...Page 1921

space ,

algebras , I . 12 . 1 ( 41 ) , ( 44 ) - Weierstrass theorem , IV . 6 . 16 ( 272 ) complex

case , IV . 6 . 17 ( 274 ) remarks on , ( 383 – 385 ) Strictly convex B - space ,

space ,

**definition**, ( 398 ) theorems on representation of Boolean rings andalgebras , I . 12 . 1 ( 41 ) , ( 44 ) - Weierstrass theorem , IV . 6 . 16 ( 272 ) complex

case , IV . 6 . 17 ( 274 ) remarks on , ( 383 – 385 ) Strictly convex B - space ,

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero