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Page 229
... coefficients a , are given by the for- mulas ap 1 f ( a ) 2лi Тc ( α —≈0 ) р + 1 -- da , p = 0 , ± 1 , ± 2 , ... , where C is any closed rectifiable Jordan curve in the annulus < ≈≈0 < ẞ which separates the circles 2-20 = = ∞ and 2 ...
... coefficients a , are given by the for- mulas ap 1 f ( a ) 2лi Тc ( α —≈0 ) р + 1 -- da , p = 0 , ± 1 , ± 2 , ... , where C is any closed rectifiable Jordan curve in the annulus < ≈≈0 < ẞ which separates the circles 2-20 = = ∞ and 2 ...
Page 359
... coefficient of f , then f2 < ∞ . ∞ 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 ] ...
... coefficient of f , then f2 < ∞ . ∞ 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 ] ...
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
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ