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Page 777
... ( Russian ) Math . Rev. 11 , 670 ( 1950 ) . On the trace formula in perturbation theory . Mat . Sbornik N. S. 33 ( 75 ) , 597-626 ( 1953 ) . ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . 8 . 9 . 10 . 11 . 12 . 13 . 15 . The theory of self ...
... ( Russian ) Math . Rev. 11 , 670 ( 1950 ) . On the trace formula in perturbation theory . Mat . Sbornik N. S. 33 ( 75 ) , 597-626 ( 1953 ) . ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . 8 . 9 . 10 . 11 . 12 . 13 . 15 . The theory of self ...
Page 781
... ( Russian ) Math . Rev. 11 , 720 ( 1950 ) . 4. Proof of the theorem on the expansion in eigenfunctions of self - adjoint differential operators . Doklady Akad . Nauk SSSR ( N. S. ) 73 , 651-654 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ...
... ( Russian ) Math . Rev. 11 , 720 ( 1950 ) . 4. Proof of the theorem on the expansion in eigenfunctions of self - adjoint differential operators . Doklady Akad . Nauk SSSR ( N. S. ) 73 , 651-654 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ...
Page 811
... ( Russian ) Math . Rev. 14 , 882 ( 1953 ) . 16 . Operators with degenerate characteristic functions . Doklady Akad . Nauk SSSR ( N. S. ) 93 , 985-988 ( 1953 ) . ( Russian ) Math . Rev. 15 , 803 ( 1954 ) . 17. Completely continuous ...
... ( Russian ) Math . Rev. 14 , 882 ( 1953 ) . 16 . Operators with degenerate characteristic functions . Doklady Akad . Nauk SSSR ( N. S. ) 93 , 985-988 ( 1953 ) . ( Russian ) Math . Rev. 15 , 803 ( 1954 ) . 17. Completely continuous ...
Contents
A Settheoretic Preliminaries | 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 Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ