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 complex ...
... 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 complex ...
Page 741
... differential equations of arbitrary order ; general boundary- value problems for elliptic equations . Proc . Nat . Acad . Sci . U.S.A. 39 , 185-190 ( 1953 ) . 5. Strongly elliptic systems of differential equations . Contributions to the ...
... differential equations of arbitrary order ; general boundary- value problems for elliptic equations . Proc . Nat . Acad . Sci . U.S.A. 39 , 185-190 ( 1953 ) . 5. Strongly elliptic systems of differential equations . Contributions to the ...
Page 762
... differential equations of second order . Duke Math . J. 14 , 323-326 ( 1947 ) . Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . On differential equations with ...
... differential equations of second order . Duke Math . J. 14 , 323-326 ( 1947 ) . Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . On differential equations with ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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