Linear Operators: General theory |
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Page 88
... condition is sufficient . Bonsall [ 1 ] showed that the separa- bility condition cannot be dropped . Ingleton [ 1 ] has given conditions ... boundary value problems . We refer the reader to the papers of Garabedian [ 1 ] , Garabedian and ...
... condition is sufficient . Bonsall [ 1 ] showed that the separa- bility condition cannot be dropped . Ingleton [ 1 ] has given conditions ... boundary value problems . We refer the reader to the papers of Garabedian [ 1 ] , Garabedian and ...
Page 788
... boundary value problem as the interval becomes infinite . Trans . Amer . Math . Soc . 30 , 797–802 ( 1928 ) . On the ... conditions for discreteness of the spectrum of self - adjoint differential equations of second order . Trudy Moskov ...
... boundary value problem as the interval becomes infinite . Trans . Amer . Math . Soc . 30 , 797–802 ( 1928 ) . On the ... conditions for discreteness of the spectrum of self - adjoint differential equations of second order . Trudy Moskov ...
Page 822
... boundary conditions . Bull . Amer . Math . Soc . 48 , 692-704 ( 1942 ) . Widder , D. V. ( see also Hirschman , I. I. ) 1. The Laplace transform . Princeton Univ . Press , Princeton , 1941 . 2. Inversion formulas for convolution ...
... boundary conditions . Bull . Amer . Math . Soc . 48 , 692-704 ( 1942 ) . Widder , D. V. ( see also Hirschman , I. I. ) 1. The Laplace transform . Princeton Univ . Press , Princeton , 1941 . 2. Inversion formulas for convolution ...
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