Linear Operators: General theory |
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Page 229
... coefficients a , are given by the for- mulas ар 1 f ( a ) 2лi Jc ( α - 20 ) +1 da , p = 0 , ± 1 , ± 2 , ... , = where C is any closed rectifiable Jordan curve in the annulus x < z - zo < ẞ which separates the circles z - zoa and z ...
... coefficients a , are given by the for- mulas ар 1 f ( a ) 2лi Jc ( α - 20 ) +1 da , p = 0 , ± 1 , ± 2 , ... , = where C is any closed rectifiable Jordan curve in the annulus x < z - zo < ẞ which separates the circles z - zoa and z ...
Page 359
... coefficient of f , then f2 < ∞ . 14 The nth Fourier coefficient of a function in L , 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 L , 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. Dirichlet's problem for linear elliptic partial differential equations . Math . Scand . 1 , 55-72 ( 1953 ) . 3 . 4 . Le problème de Dirichlet pour les équations aux dérivées partielles ...
... coefficients . Acta Math . 85 , 2-62 ( 1950 ) . 2. Dirichlet's problem for linear elliptic partial differential equations . Math . Scand . 1 , 55-72 ( 1953 ) . 3 . 4 . Le problème de Dirichlet pour les équations aux dérivées partielles ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ