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Page 743
... transformations in Hilbert space . Duke J. Math . 7 , 504-508 ( 1940 ) . Cameron , R. H. 1. A " Simpson's Rule " for the numerical evaluation of Wiener's integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . 3 . 4 ...
... transformations in Hilbert space . Duke J. Math . 7 , 504-508 ( 1940 ) . Cameron , R. H. 1. A " Simpson's Rule " for the numerical evaluation of Wiener's integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . 3 . 4 ...
Page 761
... transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . Measure Theory . D. Van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . 7. Finite ...
... transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . Measure Theory . D. Van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . 7. Finite ...
Page 783
... transformations in certain vector spaces . Bull . Amer . Math . Soc . 45 , 564-569 ( 1939 ) . On a calculus of ... transformations in reflexive vector spaces . Trans . Amer . Math . Soc . 49 , 18-40 ( 1941 ) . Means of iterated ...
... transformations in certain vector spaces . Bull . Amer . Math . Soc . 45 , 564-569 ( 1939 ) . On a calculus of ... transformations in reflexive vector spaces . Trans . Amer . Math . Soc . 49 , 18-40 ( 1941 ) . Means of iterated ...
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