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Page 741
... Proc . Nat . Acad . Sci . U.S.A. 38 , 230–235 ( 1952 ) . 2. The Dirichlet and vibration problems for linear elliptic differential equations of arbitrary order . Proc . Nat . Acad . Sci . U.S.A. 38 , 741-747 ( 1952 ) . 3. Assumption of ...
... Proc . Nat . Acad . Sci . U.S.A. 38 , 230–235 ( 1952 ) . 2. The Dirichlet and vibration problems for linear elliptic differential equations of arbitrary order . Proc . Nat . Acad . Sci . U.S.A. 38 , 741-747 ( 1952 ) . 3. Assumption of ...
Page 768
... Proc . Amer . Math . Soc . 3 , 874-883 ( 1952 ) . Izumi , S. 1 . 2 . 4 . On the bilinear functionals . Tôhoku Math . J. 42 , 195–209 ( 1936 ) . On the compactness of a class of functions . Proc . Imp . Acad . Tokyo 15 , 111-113 ( 1939 ) ...
... Proc . Amer . Math . Soc . 3 , 874-883 ( 1952 ) . Izumi , S. 1 . 2 . 4 . On the bilinear functionals . Tôhoku Math . J. 42 , 195–209 ( 1936 ) . On the compactness of a class of functions . Proc . Imp . Acad . Tokyo 15 , 111-113 ( 1939 ) ...
Page 770
... Proc . Second Berkeley Symposium Math . Statistics and Prob . , 189-215 ( 1951 ) . Kaczmarz , S. , and Steinhaus , H ... Proc . Imp . Acad . Tokyo 13 , 93-94 ( 1937 ) . 2 . 3 . 4 . Weak topology and regularity of Banach spaces . Proc ...
... Proc . Second Berkeley Symposium Math . Statistics and Prob . , 189-215 ( 1951 ) . Kaczmarz , S. , and Steinhaus , H ... Proc . Imp . Acad . Tokyo 13 , 93-94 ( 1937 ) . 2 . 3 . 4 . Weak topology and regularity of Banach spaces . Proc ...
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