## Linear Operators: Spectral theory |

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Page 1749

+ Az ox , ' V ( 0 , X1 , X2 , X3 ) = Vo ( X1 , X2 , X3 ) , where V = [ V1 , V2 , V3 ] is a

complex three - dimensional

the imaginary unit i times the magnetic

+ Az ox , ' V ( 0 , X1 , X2 , X3 ) = Vo ( X1 , X2 , X3 ) , where V = [ V1 , V2 , V3 ] is a

complex three - dimensional

**vector**equal to the sum of the “ electric ”**vector**andthe imaginary unit i times the magnetic

**vector**, and where the matrices A1 , A2 ...Page 1837

Bicontinuous linear transformations in certain

Soc . 45 , 564 - 569 ( 1939 ) . On a calculus of operators in reflexive

spaces . Trans . Amer . Math . Soc . 45 , 217 - 234 ( 1939 ) . The Cauchy -

Schwarz ...

Bicontinuous linear transformations in certain

**vector**spaces . Bull . Amer . Math .Soc . 45 , 564 - 569 ( 1939 ) . On a calculus of operators in reflexive

**vector**spaces . Trans . Amer . Math . Soc . 45 , 217 - 234 ( 1939 ) . The Cauchy -

Schwarz ...

Page 1849

1 . On the one - dimensional translation group and semi - group in certain

function spaces . Dissertation , University of Uppsala ( 1950 ) . Math . Rev . 12 ,

108 ( 1951 ) . Ogasawara , T . 1 . Compact metric Boolean algebras and

lattices .

1 . On the one - dimensional translation group and semi - group in certain

function spaces . Dissertation , University of Uppsala ( 1950 ) . Math . Rev . 12 ,

108 ( 1951 ) . Ogasawara , T . 1 . Compact metric Boolean algebras and

**vector**lattices .

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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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