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 ≤ 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 Yo there exists a unique solution matrix Y ( t ) such that Y ( to ) Yo . Show that a set of solution vectors y ( t ) , ... , y ( t ) of dy / dt = A ( t ) y form a basis for the solution space if and only if they form ...
... ( constant ) matrix Yo there exists a unique solution matrix Y ( t ) such that Y ( to ) Yo . Show that a set of solution vectors y ( t ) , ... , y ( t ) of dy / dt = A ( t ) y form a basis for the solution space if and only if they form ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ