## Linear Operators, Part 1 |

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Page 227

The same use of functionals proves the Cauchy integral

da , 2ni B0-2 where z is a point of the bounded open set U whose boundary B

consists of a finite number of closed rectifiable Jordan curves oriented in the ...

The same use of functionals proves the Cauchy integral

**formula**: 1 tra f ( a ) | ( 2 )da , 2ni B0-2 where z is a point of the bounded open set U whose boundary B

consists of a finite number of closed rectifiable Jordan curves oriented in the ...

Page 228

U ,, ... , Um . Just as in the classical one variable case we can prove , using this

Cauchy integral

of Weierstrass : Let ' n be a uniformly bounded sequence of vector valued ...

U ,, ... , Um . Just as in the classical one variable case we can prove , using this

Cauchy integral

**formula**in several variables , the following convergence theoremof Weierstrass : Let ' n be a uniformly bounded sequence of vector valued ...

Page 407

There exists a corresponding Wiener - integral

more general parabolic initial value problem . a 1 22 [ * ] F ( x , t ) F ( x , t ) + V ( x ,

t ) F ( x , t ) , t = 0 ; at 4 əx2 F ( x , 0 ) = f ( x ) , V being a given coefficient function .

There exists a corresponding Wiener - integral

**formula**for the solution F of themore general parabolic initial value problem . a 1 22 [ * ] F ( x , t ) F ( x , t ) + V ( x ,

t ) F ( x , t ) , t = 0 ; at 4 əx2 F ( x , 0 ) = f ( x ) , V being a given coefficient function .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 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

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero