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... T. Schwartz Vol . VIII : Modern Geometrical Optics By Max Herzberger Vol . IX : Orthogonal Expansions By G. Sansone Additional volumes in preparation PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs Preliminary Concepts.
... T. Schwartz Vol . VIII : Modern Geometrical Optics By Max Herzberger Vol . IX : Orthogonal Expansions By G. Sansone Additional volumes in preparation PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs Preliminary Concepts.
Page 16
... applying to the pair f1 , 4 , the procedure applied to fo . u , and then continuing inductively , one obtains a sequence F¡ , i = 1 , 2 , . . . , of real continuous functions on X , with the properties : and f ( x ) − Σ F , ( x ) ...
... applying to the pair f1 , 4 , the procedure applied to fo . u , and then continuing inductively , one obtains a sequence F¡ , i = 1 , 2 , . . . , of real continuous functions on X , with the properties : and f ( x ) − Σ F , ( x ) ...
Page 81
... applied these results to a large number of special spaces . The first really general proofs of Theorems 1.11 and 1.13 were given by Hildebrandt [ 2 ] in the case of a B - space . Banach and Steinhaus [ 1 ; p , 53 ] observed that in the ...
... applied these results to a large number of special spaces . The first really general proofs of Theorems 1.11 and 1.13 were given by Hildebrandt [ 2 ] in the case of a B - space . Banach and Steinhaus [ 1 ; p , 53 ] observed that in the ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ