Linear Operators: General theory |
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Page 565
... solution matrix of dy / dt A ( t ) Y which is non - singular . Show that the set of all non - singular matrix solutions are precisely the matrices Y ( t ) C where C is any n × n constant , non- singular matrix . 26 Let A ( t ) have ...
... solution matrix of dy / dt A ( t ) Y which is non - singular . Show that the set of all non - singular matrix solutions are precisely the matrices Y ( t ) C where C is any n × n constant , non- singular matrix . 26 Let A ( t ) have ...
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 777
... Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ( N. S. ) 76 , 21-24 ( 1951 ) . ( Russian ) Math . Rev. 12 , 613 ( 1951 ) . On certain problems on the maximum and minimum of characteristic values and on the ...
... Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ( N. S. ) 76 , 21-24 ( 1951 ) . ( Russian ) Math . Rev. 12 , 613 ( 1951 ) . On certain problems on the maximum and minimum of characteristic values and on 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 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ