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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 Fall of whose negative Fourier coefficients vanish . D 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 Fall of whose negative Fourier coefficients vanish . D 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 f in H , 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 f in H , can be written as a product gh , where g and h are in H2 . ( Hint : Use Exercise 88. ) 90 ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ