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Page 369
... constant of absolute value 1 , C is a set of at most n + 1 points -1 ≤t ≤ t2 ... < tz ≤ 1 , and there are constants C1 , ... , C with 1 c ; = f , and in terms of which we may write an " interpolation formula " k f ( x ) = Σc ; x ( t ...
... constant of absolute value 1 , C is a set of at most n + 1 points -1 ≤t ≤ t2 ... < tz ≤ 1 , and there are constants C1 , ... , C with 1 c ; = f , and in terms of which we may write an " interpolation formula " k f ( x ) = Σc ; x ( t ...
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 ( p ( s ) ) converges ...
... 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 ( p ( s ) ) converges ...
Page 564
... ( constant ) matrix Y , there exists a unique solution matrix Y ( t ) such that Y ( t ) = Yo . Show that a set of solution vectors y1 ( 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 ( t ) = Yo . Show that a set of solution vectors y1 ( t ) ,.・・・ Yn ( t ) of dy / dt A ( t ) y form a basis for the solution space if and only if they ...
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ