Linear Operators: General theory |
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Page 756
... differential equations by the Hahn - Banach Theorem . Trans . Amer . Math . Soc . 76 , 288-299 ( 1954 ) . Gårding , L. 1. Linear hyperbolic partial differential equations with constant coefficients . Acta Math . 85 , 2-62 ( 1950 ) . 2 ...
... differential equations by the Hahn - Banach Theorem . Trans . Amer . Math . Soc . 76 , 288-299 ( 1954 ) . Gårding , L. 1. Linear hyperbolic partial differential equations with constant coefficients . Acta Math . 85 , 2-62 ( 1950 ) . 2 ...
Page 781
... operators to linear differential equations of the second order . Uspehi Matem . Nauk ( N. S. ) 4 , no . 1 ( 29 ) , 3-112 ( 1949 ) . ( Russian ) Math . Rev. 11 , 116 ( 1950 ) . Amer . Math . Soc . Translation no . 59 ( 1951 ) . 2 ...
... operators to linear differential equations of the second order . Uspehi Matem . Nauk ( N. S. ) 4 , no . 1 ( 29 ) , 3-112 ( 1949 ) . ( Russian ) Math . Rev. 11 , 116 ( 1950 ) . Amer . Math . Soc . Translation no . 59 ( 1951 ) . 2 ...
Page 794
... operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 105 ( 1941 ) . 9. On the spectrum of singular non - self - adjoint differential operators of the second order . Doklady ...
... operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 105 ( 1941 ) . 9. On the spectrum of singular non - self - adjoint differential operators of the second order . Doklady ...
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