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Page 737
... values in a Banach space . Trans . Amer . Math . Soc . 38 , 357-378 ( 1935 ) . 5 . A note on topological groups . Compositio Math . 3 , 427–430 ( 1936 ) ... Boundary value and expansion problems of ordinary linear differential REFERENCES 737.
... values in a Banach space . Trans . Amer . Math . Soc . 38 , 357-378 ( 1935 ) . 5 . A note on topological groups . Compositio Math . 3 , 427–430 ( 1936 ) ... Boundary value and expansion problems of ordinary linear differential REFERENCES 737.
Page 741
... boundary values and the Green's function in the Dirichlet problem for the general linear elliptic equation . Proc ... boundary- value problems for elliptic equations . Proc . Nat . Acad . Sci . U.S.A. 39 , 185-190 ( 1953 ) . 5. Strongly ...
... boundary values and the Green's function in the Dirichlet problem for the general linear elliptic equation . Proc ... boundary- value problems for elliptic equations . Proc . Nat . Acad . Sci . U.S.A. 39 , 185-190 ( 1953 ) . 5. Strongly ...
Page 763
... boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave equations . Amer . J. Math . 72 , 849-862 ( 1950 ) . Hartman , P. , and Wintner , A. 1. The ( L2 ) -space of relative ...
... boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave equations . Amer . J. Math . 72 , 849-862 ( 1950 ) . Hartman , P. , and Wintner , A. 1. The ( L2 ) -space of relative ...
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