Fritz John
Encyclopedia
Fritz John was a German
-born mathematician
specialising in partial differential equations and ill-posed problems
. His early work was on the Radon transform
and he is remembered for John's equation
.
where he was influenced by Richard Courant
among others. With Hitler
's rise to power in 1933
"non-aryans
" were being expelled from teaching posts, and John emigrated from Germany and immigrated to England
. From then until 1991, he never returned to Germany.
John published his first paper in 1934 on Morse theory
. He was awarded his doctorate in 1934 with a thesis entitled Determining a function from its integrals over certain manifolds from Göttingen. With Richard Courant's assistance he spent a year at St John's College, Cambridge
. During this time he published papers on the Radon transform, a theme to which he would return.
John was appointed an assistant professor at the University of Kentucky
in 1935 and he emigrated to the United States
becoming naturalised in 1941. He stayed at Kentucky until 1946 apart from 1943 to 1945 during which he did war service for the Ballistic Research Laboratory
at the Aberdeen Proving Ground, Maryland. In 1946 he moved to New York University
where he remained.
Throughout the 1940s and 1950s he continued to work on the Radon transform
in particular its application to linear partial differential equation
s, convex geometry
, and the mathematical theory of water waves. He also wrote on numerical analysis
and ill-posed problems. His textbook on partial differential equations was much influential and was re-edited many times.
From the mid 1950s he started working on the theory of equilibrium nonlinear elasticity
. He retired in 1981 but continued to work on nonlinear waves.
He received many awards during his career including the Birkhoff Prize in Applied Mathematics in 1973 and the Steele Prize in 1982.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
-born mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
specialising in partial differential equations and ill-posed problems
Well-posed problem
The mathematical term well-posed problem stems from a definition given by Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that# A solution exists# The solution is unique...
. His early work was on the Radon transform
Radon transform
thumb|right|Radon transform of the [[indicator function]] of two squares shown in the image below. Lighter regions indicate larger function values. Black indicates zero.thumb|right|Original function is equal to one on the white region and zero on the dark region....
and he is remembered for John's equation
John's equation
John's equation is an ultrahyperbolic partial differential equation satisfied by the X-ray transform of a function. It is named after Fritz John....
.
Biography
He studied mathematics from 1929 to 1933 in GöttingenGeorg-August University of Göttingen
The University of Göttingen , known informally as Georgia Augusta, is a university in the city of Göttingen, Germany.Founded in 1734 by King George II of Great Britain and the Elector of Hanover, it opened for classes in 1737. The University of Göttingen soon grew in size and popularity...
where he was influenced by Richard Courant
Richard Courant
Richard Courant was a German American mathematician.- Life :Courant was born in Lublinitz in the German Empire's Prussian Province of Silesia. During his youth, his parents had to move quite often, to Glatz, Breslau, and in 1905 to Berlin. He stayed in Breslau and entered the university there...
among others. With Hitler
Adolf Hitler
Adolf Hitler was an Austrian-born German politician and the leader of the National Socialist German Workers Party , commonly referred to as the Nazi Party). He was Chancellor of Germany from 1933 to 1945, and head of state from 1934 to 1945...
's rise to power in 1933
"non-aryans
Aryan race
The Aryan race is a concept historically influential in Western culture in the period of the late 19th century and early 20th century. It derives from the idea that the original speakers of the Indo-European languages and their descendants up to the present day constitute a distinctive race or...
" were being expelled from teaching posts, and John emigrated from Germany and immigrated to England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
. From then until 1991, he never returned to Germany.
John published his first paper in 1934 on Morse theory
Morse theory
In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a differentiable function on a manifold will, in a typical case, reflect...
. He was awarded his doctorate in 1934 with a thesis entitled Determining a function from its integrals over certain manifolds from Göttingen. With Richard Courant's assistance he spent a year at St John's College, Cambridge
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
. During this time he published papers on the Radon transform, a theme to which he would return.
John was appointed an assistant professor at the University of Kentucky
University of Kentucky
The University of Kentucky, also known as UK, is a public co-educational university and is one of the state's two land-grant universities, located in Lexington, Kentucky...
in 1935 and he emigrated to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
becoming naturalised in 1941. He stayed at Kentucky until 1946 apart from 1943 to 1945 during which he did war service for the Ballistic Research Laboratory
Ballistic Research Laboratory
The Ballistic Research Laboratory at Aberdeen Proving Ground, Maryland was the center for the United States Army's research efforts in ballistics and vulnerability/lethality analysis....
at the Aberdeen Proving Ground, Maryland. In 1946 he moved to New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
where he remained.
Throughout the 1940s and 1950s he continued to work on the Radon transform
in particular its application to linear partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s, convex geometry
Convex geometry
Convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming,...
, and the mathematical theory of water waves. He also wrote on numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
and ill-posed problems. His textbook on partial differential equations was much influential and was re-edited many times.
From the mid 1950s he started working on the theory of equilibrium nonlinear elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
. He retired in 1981 but continued to work on nonlinear waves.
He received many awards during his career including the Birkhoff Prize in Applied Mathematics in 1973 and the Steele Prize in 1982.
See also
- Bounded mean oscillationBounded mean oscillationIn harmonic analysis, a function of bounded mean oscillation, also known as a BMO function, is a real-valued function whose mean oscillation is bounded...
- Fritz John conditionsFritz John conditionsThe Fritz John conditions , in mathematics, are a necessary condition for a solution in nonlinear programming to be optimal...
- John ellipsoidJohn ellipsoidIn mathematics, the John ellipsoid E associated to a convex body K in n-dimensional Euclidean space Rn is the ellipsoid of maximal n-dimensional volume contained within K. The John ellipsoid is named after the German mathematician Fritz John...
- John transform