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 Exercise 34. ( Heref is in Lp , AC , or
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 , or
C \ 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 Exercise 53 maps H , in a linear one - one
manner onto the closed subspace of L , consisting of those F all of whose
negative Fourier coefficients vanish . 55 Using the notations of Exercises 53 and
54 , show ...
Show that the map : f f defined in Exercise 53 maps H , in a linear one - one
manner onto the closed subspace of L , consisting of those F all of whose
negative Fourier coefficients vanish . 55 Using the notations of Exercises 53 and
54 , show ...
Page 371
86 Let p , f be as in Exercise 85. Then ( ei ) + 0 for almost all 0 . 87 Let p > 1 and
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 and
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 ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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