Per Enflo
| Per Enflo | |
|---|---|
 |
|
| Born |
20 May 1944 , Sweden |
| Residence | Kent, Ohio, United States |
| Fields |
Functional analysis Operator theory Analytic number theory |
| Institutions |
University of California, Berkeley Stanford University École Polytechnique, Paris The Royal Institute of Technology, Kent State University |
| Alma mater | |
| Doctoral advisor | Hans Rådström |
| Doctoral students | Nilson Bernardes Miguel Lacruz Jan-Ove Larsson Marie Lövblom Bruce Reznick Anthony Weston |
| Known for |
Approximation problem Schauder basis Hilbert's fifth problem (infinite-dimensional) uniformly convex renorms of super-reflexive Banach spaces embedding metric spaces (unbounded distortion of cube) "Concentration" of polynomials at low degree Invariant subspace problem |
| Influences |
Joram Lindenstrauss Laurent Schwartz |
| Influenced | Bernard Beauzamy |
| Notable awards | Mazur's "live goose" for solving "Scottish Book" Problem 153 |
Per H. Enflo (Swedish: [ˌpæːɹ ˈeːnfluː]; born 20 May 1944) is a mathematician who has solved fundamental problems in functional analysis. Three of these problems had been open for more than forty years:
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 Miller Institute for Basic Research in Science at the University of California, Berkeley, Stanford University, École Polytechnique, (Paris) and The Royal Institute of Technology, .
Enflo is also a concert pianist.
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, , and time-series analysis. Besides studying spaces of functions, functional analysis also studies the continuous linear operators on spaces of functions.
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