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Page 629
... solution in C [ 0 , ∞ ] for each xe C [ 0 , ∞o ] . In this case y R ( 2 ; A ) x . Consideration of the general solution of this differential equation shows σ ( A ) is the half plane R ( 2 ) ≤ 0 , and - R ( 2 ; A ) ( x , t ) = [ * e ...
... solution in C [ 0 , ∞ ] for each xe C [ 0 , ∞o ] . In this case y R ( 2 ; A ) x . Consideration of the general solution of this differential equation shows σ ( A ) is the half plane R ( 2 ) ≤ 0 , and - R ( 2 ; A ) ( x , t ) = [ * e ...
Page 762
... solutions of linear 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 . 6 ...
... solutions of linear 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 . 6 ...
Page 763
... solutions of real linear differential equations of second order . Amer . J. Math . 70 , 1-10 ( 1948 ) . 4 . Criteria for ... solution of linear differential equations of second order . Amer . J. Math . 77 , 475-483 ( 1955 ) . On linear ...
... solutions of real linear differential equations of second order . Amer . J. Math . 70 , 1-10 ( 1948 ) . 4 . Criteria for ... solution of linear differential equations of second order . Amer . J. Math . 77 , 475-483 ( 1955 ) . On linear ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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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 Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ