Linear Operators: General theory |
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Page 369
... constant of absolute value 1 , C is a ≤ t2 ... < tx ≤ 1 , and there are -- set of at most n + 1 points -1 ≤ħ constants C1 , . . . , Ck with Σ - 1 C1 | write an " interpolation formula " k = f ( x ) = Σc , x ( t ) , j = 1 If , and in ...
... constant of absolute value 1 , C is a ≤ t2 ... < tx ≤ 1 , and there are -- set of at most n + 1 points -1 ≤ħ constants C1 , . . . , Ck with Σ - 1 C1 | write an " interpolation formula " k = f ( x ) = Σc , x ( t ) , j = 1 If , and in ...
Page 516
... constant factor if and only if n - 1 Σf ( ' ( s ) ) converges uniformly to a constant for each fe B ( S ) . n - 1 i = 0 43 Show that in Exercise 39 the measure μ is unique up to a positive constant factor if and only if n - 1 ( ' ( s ) ...
... constant factor if and only if n - 1 Σf ( ' ( s ) ) converges uniformly to a constant for each fe B ( S ) . n - 1 i = 0 43 Show that in Exercise 39 the measure μ is unique up to a positive constant factor if and only if n - 1 ( ' ( s ) ...
Page 565
... constant , non- singular matrix . 26 Let A ( t ) have period p > 0 ; that is , A ( t + p ) = A ( t ) for all ton - ∞ < t < ∞o . If Y ( t ) is a non - singular solution matrix of dy / dt = A ( t ) Y then show that Y ( t + p ) = Y ( t ) ...
... constant , non- singular matrix . 26 Let A ( t ) have period p > 0 ; that is , A ( t + p ) = A ( t ) for all ton - ∞ < t < ∞o . If Y ( t ) is a non - singular solution matrix of dy / dt = A ( t ) Y then show that Y ( t + p ) = Y ( t ) ...
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