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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 , μ the procedure applied to fo , Mo , and then continuing inductively , one obtains a sequence F1 , i = 1 , 2 , . . . , of real continuous functions on X , with the properties : and n \ f ( x ) − Σ F , ( x ) ...
... applying to the pair f1 , μ the procedure applied to fo , Mo , and then continuing inductively , one obtains a sequence F1 , i = 1 , 2 , . . . , of real continuous functions on X , with the properties : and n \ 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 |
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