Linear Operators: General theory |
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Page 229
... coefficients a , are given by the for- mulas 1 ap = Σπί f ( x ) c ( α - 20 ) +1 da , p = 0 , ± 1 , ± 2 , .. a - where C is any closed rectifiable Jordan curve in the annulus α < zzo < ẞ which separates the circles z - zo = x and z ― z ...
... coefficients a , are given by the for- mulas 1 ap = Σπί f ( x ) c ( α - 20 ) +1 da , p = 0 , ± 1 , ± 2 , .. a - where C is any closed rectifiable Jordan curve in the annulus α < zzo < ẞ which separates the circles z - zo = x and z ― z ...
Page 359
... coefficient of f , then < ∞ . ∞ 14 The nth Fourier coefficient of a function in L1 approaches zero as n approaches infinity . 15 Show that the Fourier series of some continuous function fails to converge uniformly on [ 0 , 27 ] . Show ...
... coefficient of f , then < ∞ . ∞ 14 The nth Fourier coefficient of a function in L1 approaches zero as n approaches infinity . 15 Show that the Fourier series of some continuous function fails to converge uniformly on [ 0 , 27 ] . Show ...
Page 756
... coefficients . Acta Math . 85 , 2-62 ( 1950 ) . 2 . 3 . Dirichlet's problem for linear elliptic partial differential equations . Math . Scand . 1 , 55–72 ( 1953 ) . Le problème de Dirichlet pour les équations aux dérivées partielles ...
... coefficients . Acta Math . 85 , 2-62 ( 1950 ) . 2 . 3 . Dirichlet's problem for linear elliptic partial differential equations . Math . Scand . 1 , 55–72 ( 1953 ) . Le problème de Dirichlet pour les équations aux dérivées partielles ...
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 converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ