Linear Operators: General theory |
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Page 229
... coefficients a , are given by the for- mulas ap 1 f ( x ) 2лi Jc ( α - 20 ) + 1` da , p = 0 , ± 1 , ± 2 , .. where C is any closed rectifiable Jordan curve in the annulus a < │≈ - 20 < ẞ which separates the circles 2-20 = α and ...
... coefficients a , are given by the for- mulas ap 1 f ( x ) 2лi Jc ( α - 20 ) + 1` da , p = 0 , ± 1 , ± 2 , .. where C is any closed rectifiable Jordan curve in the annulus a < │≈ - 20 < ẞ which separates the circles 2-20 = α and ...
Page 359
... coefficient of f , then f < ∞ . 00 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 f < ∞ . 00 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 . 4 . 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 . 4 . 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 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