Linear Operators: General theory |
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Page 564
... solution y ( t ) such that y ( t ) = yo 20 Show that the solutions of dy / dt sional complex linear vector space . 21 = = A ( t ) y form an n - dimen- 0 Consider the matrix differential equation dy / dt = A ( t ) Y where a solution is a ...
... solution y ( t ) such that y ( t ) = yo 20 Show that the solutions of dy / dt sional complex linear vector space . 21 = = A ( t ) y form an n - dimen- 0 Consider the matrix differential equation dy / dt = A ( t ) Y where a solution is a ...
Page 610
... solution , then they both have the same finite number of linearly independent solutions . In this case the equations ... solution for ( N ) is found by adding a particular solution of ( N ) to the general solution of ( H ) . The results ...
... solution , then they both have the same finite number of linearly independent solutions . In this case the equations ... solution for ( N ) is found by adding a particular solution of ( N ) to the general solution of ( H ) . The results ...
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 ...
Contents
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ