## Linear Operators: General theory |

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Page 140

An

the forms : [ a , b ] = { ssa SS Sb } , ( a , b ) = { sla 5 s < b } , ( a , b ] ... The number

a is called the left end point and b the right end point of any of these

An

**interval**is a set of points in the extended real number system which has one ofthe forms : [ a , b ] = { ssa SS Sb } , ( a , b ) = { sla 5 s < b } , ( a , b ] ... The number

a is called the left end point and b the right end point of any of these

**intervals**.Page 141

Şan , + 1 = bn , + 1 < cten , = an , and such that È \ | ( 61 ) - | ( az ) > d . i = n2 + 1

The argument may be repeated by defining Ez = an , - c and choosing

appropriate points in the

every integer k ...

Şan , + 1 = bn , + 1 < cten , = an , and such that È \ | ( 61 ) - | ( az ) > d . i = n2 + 1

The argument may be repeated by defining Ez = an , - c and choosing

appropriate points in the

**interval**( c , c + ag ] . By induction , it is clear that forevery integer k ...

Page 283

The proof will require the following two lemmas . 3 LEMMA . An almost periodic

function is bounded . PROOF OF LEMMA 3 . Since an almost periodic function f is

continuous , the function f ( s ) has a maximum K on the

The proof will require the following two lemmas . 3 LEMMA . An almost periodic

function is bounded . PROOF OF LEMMA 3 . Since an almost periodic function f is

continuous , the function f ( s ) has a maximum K on the

**interval**0 < x SL ( 1 ) .### 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 |

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