William Frederick Eberlein (June 25, 1917,

Shawano, Wisconsin Shawano (pronounced SHAW-no) is a city in Shawano County, Wisconsin, United States. The population was 9,305 at the 2010 census. It is the county seat of Shawano County. Geography According to the United States Census Bureau, the city has a tota ...

– 1986,

Rochester, New York Rochester () is a City (New York), city in the U.S. state of New York (state), New York, the county seat, seat of Monroe County, New York, Monroe County, and the fourth-most populous in the state after New York City, Buffalo, New York, Buffalo, ...

) was an American mathematician, specializing in mathematical analysis and mathematical physics.

Life

Eberlein studied from 1936 to 1942 at the

University of Wisconsin A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...

and at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, where he received in 1942 a PhD for the thesis ''Closure, Convexity, and Linearity in Banach Spaces'' under the direction of

Marshall Stone Marshall Harvey Stone (April 8, 1903 – January 9, 1989) was an American mathematician who contributed to real analysis, functional analysis, topology and the study of Boolean algebras. Biography Stone was the son of Harlan Fiske Stone, who wa ...

. He was married twice—to Mary Bernarda Barry and Patricia Ramsay James. He had four children with Mary Barry, including Patrick Barry Eberlein, another renowned mathematician. Patricia Ramsay James was a mathematician who moved into computer science as the field opened up; their one child is Kristen James Eberlein, the chair of the OASIS

Darwin Information Typing Architecture The Darwin Information Typing Architecture (DITA) specification defines a set of document types for authoring and organizing topic-oriented information, as well as a set of mechanisms for combining, extending, and constraining document types. It i ...

Technical Committee.

Work

Eberlein had academic positions at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

(1947–1948), at the University of Wisconsin (1948–1955), at

Wayne State University Wayne State University (WSU) is a public research university in Detroit, Michigan. It is Michigan's third-largest university. Founded in 1868, Wayne State consists of 13 schools and colleges offering approximately 350 programs to nearly 25,000 ...

(1955–1956), and from 1957 at the

University of Rochester The University of Rochester (U of R, UR, or U of Rochester) is a private research university in Rochester, New York. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The University of Roc ...

, where he remained for the rest of his career.A Guide to the W. F. Eberlein Papers, 1936–1986
Briscoe Center for American History, University of Texas at Austin, retrieved 2014-06-19. His doctoral students include William F. Donoghue, Jr. and

A. Wayne Wymore Albert Wayne Wymore (February 1, 1927 – February 24, 2011) was an American mathematician, systems engineer, Professor Emeritus of Systems and Industrial Engineering of the University of Arizona, and one of the founding fathers of systems engine ...

Contributions

He worked on

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...

ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

, mean value theorems, and

numerical integration In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations ...

. Eberlein also worked on spacetime models, internal symmetries in

gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...

, and

spinor In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight ...

s. His name is attached to the

Eberlein–Šmulian theorem In the mathematical field of functional analysis, the Eberlein–Šmulian theorem (named after William Frederick Eberlein and Witold Lwowitsch Schmulian) is a result that relates three different kinds of weak compactness in a Banach space. St ...

in functional analysis and the

Eberlein compacta In mathematics an Eberlein compactum, studied by William Frederick Eberlein, is a compact topological space homeomorphic to a subset of a Banach space with the weak topology. Every compact metric space, more generally every one-point compactificat ...

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

References

{{DEFAULTSORT:Eberlein, William Frederick People from Shawano, Wisconsin University of Wisconsin–Madison alumni Harvard University alumni Wayne State University faculty University of Wisconsin–Madison faculty University of Rochester faculty 20th-century American mathematicians 1917 births 1986 deaths Functional analysts