Functional AnalysisClassic exposition of modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functionals and transformations. Topics include Lebesque and Stieltjes integrals, Hilbert and Banach spaces, self-adjunct transformations, spectral theories for linear transformations of general type, more. Translated from 2nd French edition by Leo F. Boron. 1955 edition. Bibliography. |
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absolutely continuous arbitrary assume Banach Banach space belongs bounded linear transformation bounded variation C₁ characteristic function characteristic value completely continuous condition consequently consider continuous function convergence corresponding decomposition defined definition denote denumerable domain element ƒ equal exists extension space f₁ fact finite number finite rank follows formula function f(x functions of bounded ƒ and g hence Hilbert space hypothesis implies inequality infinite integral equations interval function inverse kernel Lebesgue Lebesgue integral lemma limit linear combinations linear functional linear transformation M₁ Math mation measurable function measure zero nondecreasing norm obtain obviously orthogonal particular permutable polynomial positive proved rectangle relation respect RIESZ self-adjoint transformation semi-group solution space H space L² spectral family spectral set spectrum step functions Stieltjes integral subspace summable function symmetric transformation T₁ theorem total variation uniformly unitary transformations valid