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Page 745
... self - adjoint differential operators . Proc . Nat . Acad . Sci . 38 , 732-737 ( 1952 ) . The spectral representation of ordinary self - adjoint differential operators . Ann . of Math . ( 2 ) 60 , 192-211 ( 1954 ) . A characterization ...
... self - adjoint differential operators . Proc . Nat . Acad . Sci . 38 , 732-737 ( 1952 ) . The spectral representation of ordinary self - adjoint differential operators . Ann . of Math . ( 2 ) 60 , 192-211 ( 1954 ) . A characterization ...
Page 780
... self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . 1. Sur la notion du groupe abstrait topologique . Fund . Math . 9 , 37-44 ( 1927 ) . Lengyel , B. A. 1. On the spectral theorem of self ...
... self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . 1. Sur la notion du groupe abstrait topologique . Fund . Math . 9 , 37-44 ( 1927 ) . Lengyel , B. A. 1. On the spectral theorem of self ...
Page 794
... self - adjoint differential operators of the second order . Doklady Akad . Nauk SSSR ( N. S. ) 85 , 41–44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . 10. Investigation of the spectrum and expansion in eigenfunctions of ...
... self - adjoint differential operators of the second order . Doklady Akad . Nauk SSSR ( N. S. ) 85 , 41–44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . 10. Investigation of the spectrum and expansion in eigenfunctions of ...
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 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ