Functional analysis 泛函分析
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内容提要：
Classic 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, much more. Translated from 2nd French edition by Leo F. Boron. 1955 edition. Bibliography.
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目录：
CHAPTER I:DIFFERENTIATION
Lebesgue s theorem on the Derivative of a Monotonlc Function Some Immediate Consequences of Lebesgues Theorem Interval Functions CHAPTER II:THE LEBESGUE INTEGRAL Definition and Fundarnental Properties Indefinite Integrals Absoluteiy Continuous Functions The Space L2 and its Linear Functionais Lp Spaaces Founctions of Senveral Vatiables Other Definitluns of the Lebesgue Integral CHAPTER III:THE STLEL TJES DNTBGRAL AND ITS GENBRALINATIONS Linear Punctionals on the spnace of Comfinuous Punctions Generalixation of the Stieftjes Integral The Daniel Integral CHAPTER IV:INTBGRAL BQUATIONS The Method of Susccehtive Approximafons The Fretholm ALterative Fredlim Determinants Anofher MEtiord Based on Ciomplete Continuity Applications to Potenthal Theory CHAPTER V:HILBERT AND BANACH SPACRS Hiltbert Space Banach Spaces CHAPTER VI:COMPLETELY CONTINUOUS SYMMETRIC TRANSFORMATIONS OF HIL BERT SPACE Existence of Characteristic Elements Theorem on Series Development Transforrnations with Symmetiic Kermel Applications to the Viforating-String Proble and to Almost Periondic Fumstions CHAPTER VII:BOUNDED SYMMETRIC UNITARY AND NORMAL transformations of hilbert space CHAPTER VIII:UNBOUNDED LINEAR TRANSPORMATIONS OF HIL BERT SPACE CHAPTER IX:SHLF-ADJOINT TRANSRORMATIONS FUNCTIONAL CALCULUS SPBCTRUM PERTURBATIONS CHAPTER X:GROUPS AND SEMIGROUPS OF TRANSFORMATIONS CHAPTER XI:SPECTRAL THEORIES FOR LINEAR TRANSFORMATIONS OF GENERAL TYPE |
