Linear Operators: General theory |
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Page 228
... derivatives of fn of arbitrarily large order converge to the corresponding partial derivatives of f uniformly in V. From this theorem , we can easily derive the useful fact that if f is analytic in the Cartesian product U1X ... XU , of ...
... derivatives of fn of arbitrarily large order converge to the corresponding partial derivatives of f uniformly in V. From this theorem , we can easily derive the useful fact that if f is analytic in the Cartesian product U1X ... XU , of ...
Page 384
... derivatives including those of order n converge uniformly to the corresponding derivatives of f . ) Of the many extensions of the Weierstrass theorem for [ 0 , 1 ] we mention the striking theorem of Müntz [ 1 ] which asserts that the ...
... derivatives including those of order n converge uniformly to the corresponding derivatives of f . ) Of the many extensions of the Weierstrass theorem for [ 0 , 1 ] we mention the striking theorem of Müntz [ 1 ] which asserts that the ...
Page 655
... derivatives f ' ' lying in L ,, and which is defined by Aff " for fe D ( A ) . 14 Let X = L ( -∞ , ∞ ) , 1 ≤ p ... derivatives and with second derivatives f " lying in L ,, and which is defined by Af = f ' ' , ƒ € D ( A ) . 16 Let X ...
... derivatives f ' ' lying in L ,, and which is defined by Aff " for fe D ( A ) . 14 Let X = L ( -∞ , ∞ ) , 1 ≤ p ... derivatives and with second derivatives f " lying in L ,, and which is defined by Af = f ' ' , ƒ € D ( A ) . 16 Let X ...
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