## Linear Operators: Spectral theory |

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Page 1050

We begin our formal development by considering a

function f defined on Euclidean n - space E " , supposing that f has a finite

number of " singularities ” at which it is not

certain ...

We begin our formal development by considering a

**Lebesgue**measurablefunction f defined on Euclidean n - space E " , supposing that f has a finite

number of " singularities ” at which it is not

**Lebesgue**integrable , and defining acertain ...

Page 1210

Q . E . D . We now turn our attention to the problem of giving an analytical

representation of the map U . This problem will be discussed under the

assumption that T is a self adjoint operator in a

which is restricted ...

Q . E . D . We now turn our attention to the problem of giving an analytical

representation of the map U . This problem will be discussed under the

assumption that T is a self adjoint operator in a

**Lebesgue**space L ( S , & , v )which is restricted ...

Page 1913

( See also Set function ) Borel or Borel -

) decomposition of . ( See Decomposition ) determined by a function , ( 142 ) , (

144 ) differentiation of , III . 12 change of , III . 10 . 8 ( 182 ) , X . I ( 894 ) definition ...

( See also Set function ) Borel or Borel -

**Lebesgue**, ( 139 ) Borel - Stieltjes , ( 142) decomposition of . ( See Decomposition ) determined by a function , ( 142 ) , (

144 ) differentiation of , III . 12 change of , III . 10 . 8 ( 182 ) , X . I ( 894 ) definition ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

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