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Page 364
... Exercises 35 and 49. ) 51 Show that if Tm is the operator of Exercise 45 , ( Tmf ) ( x ) → f ( x ) at every point of the Lebesgue set of a function fe L. Show that the same holds for the operator T , of Exercise 47. ( Hint . Use ...
... Exercises 35 and 49. ) 51 Show that if Tm is the operator of Exercise 45 , ( Tmf ) ( x ) → f ( x ) at every point of the Lebesgue set of a function fe L. Show that the same holds for the operator T , of Exercise 47. ( Hint . Use ...
Page 365
... 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 that if fe H , and if ( U ...
... 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 that if fe H , and if ( U ...
Page 371
... Exercise 85 to apply to zeros on the boundary of the unit disc . ) 88 Show that Exercise 87 is valid even if p = 1 . 89 Every function ƒ in H1 can be written as a product gh , where g and h are in H2 . ( Hint : Use Exercise 88. ) 90 ...
... Exercise 85 to apply to zeros on the boundary of the unit disc . ) 88 Show that Exercise 87 is valid even if p = 1 . 89 Every function ƒ in H1 can be written as a product gh , where g and h are in H2 . ( Hint : Use Exercise 88. ) 90 ...
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A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ