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Per H. Enflo (; born 1944) is a mathematician who has solved fundamental problems in functional analysis. Three of these problems had been open for more than forty years:〔Page 586 in Halmos 1990.〕 * The basis problem and the approximation problem〔Per Enflo: ''A counterexample to the approximation problem in Banach spaces.'' Acta Mathematica vol. 130, no. 1, Juli 1973〕 and later * the invariant subspace problem for Banach spaces.〔 * * 〕 In solving these problems, Enflo developed new techniques which were then used by other researchers in functional analysis and operator theory for years. Some of Enflo's research has been important also in other mathematical fields, such as number theory, and in computer science, especially computer algebra and approximation algorithms. Enflo works at Kent State University, where he holds the title of University Professor. Enflo has earlier held positions at the University of California, Berkeley, Stanford University, École Polytechnique, (Paris) and The Royal Institute of Technology, Stockholm. Enflo is also a concert pianist. == Enflo's contributions to functional analysis and operator theory == In mathematics, Functional analysis is concerned with the study of vector spaces and operators acting upon them. It has its historical roots in the study of functional spaces, in particular transformations of functions, such as the Fourier transform, as well as in the study of differential and integral equations. In functional analysis, an important class of vector spaces consists of the complete normed vector spaces over the real or complex numbers, which are called Banach spaces. An important example of a Banach space is a Hilbert space, where the norm arises from an inner product. Hilbert spaces are of fundamental importance in many areas, including the mathematical formulation of quantum mechanics, stochastic processes, and time-series analysis. Besides studying spaces of functions, functional analysis also studies the continuous linear operators on spaces of functions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Per Enflo」の詳細全文を読む スポンサード リンク
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