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 € I and each y 。€ En 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 € I and each y 。€ En 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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ