Linear Operators: General theory |
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Page 629
... solution in C [ 0 , ∞ ] for each a € C [ 0 , ∞ ] . In this case y = R ( 2 ; A ) x . Consideration of the general solution of this differential equation shows σ ( 4 ) is the half plane ( 2 ) ≤0 , and R ( 2 ; A ) ( x , t ) = √ * e ...
... solution in C [ 0 , ∞ ] for each a € C [ 0 , ∞ ] . In this case y = R ( 2 ; A ) x . Consideration of the general solution of this differential equation shows σ ( 4 ) is the half plane ( 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 ) . Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . On ...
... solutions of linear 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 ...
Page 763
... solutions of real linear differential equations of second order . Amer . J. Math . 70 , 1-10 ( 1948 ) . Criteria for the ... 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 ) . Criteria for the ... solution of linear differential equations of second order . Amer . J. Math . 77 , 475-483 ( 1955 ) . On linear ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ