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 ... < tx ≤ 1 , and there are constants C1 , ... , C with Σ - 1 | ci | = | f | , and in terms of which we may write an " interpolation formula " k f ( x ) ...
... constant of absolute value 1 , C is a set of at most n + 1 points -1 ≤t ≤t2 ... < tx ≤ 1 , and there are constants C1 , ... , C with Σ - 1 | ci | = | f | , and in terms of which we may write an " interpolation formula " k f ( x ) ...
Page 516
... constant factor if and only if n - 1 Σf ( ' ( 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 Σf ( p ( s ) ...
... constant factor if and only if n - 1 Σf ( ' ( 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 Σf ( p ( 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 ) C ...
... 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 ) C ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ