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Page 759
... Spectral measure . Doklady Akad . Nauk SSSR ( N. S. ) 81 , 345–348 ( 1951 ) . ( Russian ) Math . Rev. 13 , 470 ( 1952 ) . 6. Operational integral in a Banach space . Doklady Akad . Nauk SSSR ( N.S. ) 71 , 5-8 ( 1950 ) . ( Russian ) Math ...
... Spectral measure . Doklady Akad . Nauk SSSR ( N. S. ) 81 , 345–348 ( 1951 ) . ( Russian ) Math . Rev. 13 , 470 ( 1952 ) . 6. Operational integral in a Banach space . Doklady Akad . Nauk SSSR ( N.S. ) 71 , 5-8 ( 1950 ) . ( Russian ) Math ...
Page 770
... measure spaces , I , II . I. Proc . Imp . Acad . Tokyo 19 , 148–151 ( 1943 ) . II . ibid . 19 , 184-188 ( 1943 ) . An example concerning uniform boundedness of spectral measures . Pacific J. Math . 4 , 363-372 ( 1954 ) . Ergodic ...
... measure spaces , I , II . I. Proc . Imp . Acad . Tokyo 19 , 148–151 ( 1943 ) . II . ibid . 19 , 184-188 ( 1943 ) . An example concerning uniform boundedness of spectral measures . Pacific J. Math . 4 , 363-372 ( 1954 ) . Ergodic ...
Page 772
... spectral measure function , I. Il Nuovo Cimento ( 10 ) 2 , 917-961 ( 1955 ) . The determination of the scattering potential from the spectral measure function , I - III . Div . of Electromag . Res . , Inst . Math . Sci . , New York Univ ...
... spectral measure function , I. Il Nuovo Cimento ( 10 ) 2 , 917-961 ( 1955 ) . The determination of the scattering potential from the spectral measure function , I - III . Div . of Electromag . Res . , Inst . Math . Sci . , New York Univ ...
Contents
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ