Linear Operators: General theory |
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Page 564
... differential system for each te I. The theory of differential equations assures us that for each to e I and each yo e E " there exists a unique solution y ( t ) such that y ( to ) = Yo 20 Show that the solutions of dy / dt sional ...
... differential system for each te I. The theory of differential equations assures us that for each to e I and each yo e E " there exists a unique solution y ( t ) such that y ( to ) = Yo 20 Show that the solutions of dy / dt sional ...
Page 762
... differential equations of second order . Duke Math . J. 14 , 323-326 ( 1947 ) . 4. Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . 5. On differential ...
... differential equations of second order . Duke Math . J. 14 , 323-326 ( 1947 ) . 4. Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . 5. On differential ...
Page 763
... differential equations . Amer . J. Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the ...
... differential equations . Amer . J. Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the ...
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ