## Linear Operators, Part 1 |

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Page 364

1 / 2qinx , the operator Tm is given by the integral $ " ( U , f ) Km ( t ) dt , Tmi

where Km ( t ) is Km ( 0 , t ) in the notation of

C \ n ) ) . 50 Show that in case on ( x ) = ( 27 ) -1 / 2eina , Tmi f in the norm of Ly (

or ...

1 / 2qinx , the operator Tm is given by the integral $ " ( U , f ) Km ( t ) dt , Tmi

where Km ( t ) is Km ( 0 , t ) in the notation of

**Exercise**34. ( Heref is in Lp , AC , orC \ n ) ) . 50 Show that in case on ( x ) = ( 27 ) -1 / 2eina , Tmi f in the norm of Ly (

or ...

Page 365

Show that the map : f f defined in

manner onto the closed subspace of L , consisting of those F all of whose

negative Fourier coefficients vanish . 55 Using the notations of

54 , show ...

Show that the map : f f defined in

**Exercise**53 maps H , in a linear one - onemanner onto the closed subspace of L , consisting of those F all of whose

negative Fourier coefficients vanish . 55 Using the notations of

**Exercises**53 and54 , show ...

Page 371

86 Let p , f be as in

let | be a function in Hg . Then there exists a function g in H. such that g ( e ) = 1

for almost all 0 , LeHy H , 8 and such that f / g has no zeros . ( Hint : Generalize

the ...

86 Let p , f be as in

**Exercise**85. Then ( ei ) + 0 for almost all 0 . 87 Let p > 1 andlet | be a function in Hg . Then there exists a function g in H. such that g ( e ) = 1

for almost all 0 , LeHy H , 8 and such that f / g has no zeros . ( Hint : Generalize

the ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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