Linear Operators: General theory |
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Page 369
... constant of absolute value 1 , C is a set of at most n + 1 points -1 ≤t ≤ t ... < t≤1 , and there are constants c1 , . . . , C with 1 c f , and in terms of which we may write an " interpolation formula " Ck i = 1 k - f ( x ) = Σc ; x ...
... constant of absolute value 1 , C is a set of at most n + 1 points -1 ≤t ≤ t ... < t≤1 , and there are constants c1 , . . . , C with 1 c f , and in terms of which we may write an " interpolation formula " Ck i = 1 k - f ( x ) = Σc ; x ...
Page 516
... constant factor if and only if n - 1 ( p ( s ) ) converges uniformly to a constant for each fe B ( S ) . 43 Show that in Exercise 39 the measure u is unique up to a positive constant factor if and only if n - 1 Σ = 1f ( p ( s ) ...
... constant factor if and only if n - 1 ( p ( s ) ) converges uniformly to a constant for each fe B ( S ) . 43 Show that in Exercise 39 the measure u is unique up to a positive constant factor if and only if n - 1 Σ = 1f ( p ( s ) ...
Page 564
... ( constant ) matrix Y , there exists a unique solution matrix Y ( t ) such that Y ( to ) Yo . Show that a set of solution vectors y ( t ) , ... , yn ( t ) of dy / dt = A ( t ) y form a basis for the solution . space if and only if they ...
... ( constant ) matrix Y , there exists a unique solution matrix Y ( t ) such that Y ( to ) Yo . Show that a set of solution vectors y ( t ) , ... , yn ( t ) of dy / dt = A ( t ) y form a basis for the solution . space if and only if they ...
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