## Linear Operators: General theory |

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Page 195

Indeed , according to Tonelli ' s theorem , both these

that the product of measures is commutative . ) Generalizing this statement , and

...

Indeed , according to Tonelli ' s theorem , both these

**integrals**are equal to the**integral**off with respect to the product measure ( and we have already remarkedthat the product of measures is commutative . ) Generalizing this statement , and

...

Page 227

Let f be analytic in V - A . Then the second form of Cauchy ' s

states : If we agree to orient the Jordan ... and is independent of any particular

choice of the neighborhood U of A . In other words , the

...

Let f be analytic in V - A . Then the second form of Cauchy ' s

**integral**theoremstates : If we agree to orient the Jordan ... and is independent of any particular

choice of the neighborhood U of A . In other words , the

**integrals**SB and SB , are...

Page 743

On the existence of certain singular

numerical evaluation of Wiener ' s

111 - 130 ( 1951 ) . The first variation of an indefinite Wiener

On the existence of certain singular

**integrals**. ... A “ Simpson ' s Rule ” for thenumerical evaluation of Wiener ' s

**integrals**in function space . Duke Math . J . 18 ,111 - 130 ( 1951 ) . The first variation of an indefinite Wiener

**integral**. Proc .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 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 Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math mean measure space metric neighborhood norm positive measure problem Proc projection PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero