Lipót Fejér
Encyclopedia
Lipót Fejér (February 9, 1880, Pécs
– October 15, 1959, Budapest
) was a Hungarian
mathematician
. Fejér was born Leopold Weiss, and changed to the Hungarian name Fejér around 1900.
Fejér studied mathematics and physics in Budapest and Berlin, where he was taught by Hermann Schwarz
. From 1902 to 1905 Fejér taught at the University of Pázmány Péter and from 1905 until 1911 he taught at Kolozsvár in Hungary
(now Cluj-Napoca
in Romania
). In 1911 Fejér was appointed to the chair of mathematics at the University of Budapest and he held that post until his death. He was elected corresponding member (1908), member (1930) of the Hungarian Academy of Sciences
.
During his period in the chair at Budapest Fejér led a highly successful Hungarian school of analysis. He was the thesis advisor of mathematicians such as John von Neumann
, Paul Erdős
, George Pólya
and Pál Turán
.
Lipót Fejér is buried in Kerepesi Cemetery
in Budapest.
Fejér's research concentrated on harmonic analysis
and, in particular, Fourier series
.
Fejér collaborated to produce important papers, one with Carathéodory
on entire function
s in 1907 and another major work with Frigyes Riesz
in 1922 on conformal map
pings (specifically, a short proof of the Riemann mapping theorem).
In the same article Pólya writes about Fejér's style of mathematics:
Pécs
Pécs is the fifth largest city of Hungary, located on the slopes of the Mecsek mountains in the south-west of the country, close to its border with Croatia. It is the administrative and economical centre of Baranya county...
– October 15, 1959, Budapest
Budapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
) was a Hungarian
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
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....
. Fejér was born Leopold Weiss, and changed to the Hungarian name Fejér around 1900.
Fejér studied mathematics and physics in Budapest and Berlin, where he was taught by Hermann Schwarz
Hermann Schwarz
Karl Hermann Amandus Schwarz was a German mathematician, known for his work in complex analysis. He was born in Hermsdorf, Silesia and died in Berlin...
. From 1902 to 1905 Fejér taught at the University of Pázmány Péter and from 1905 until 1911 he taught at Kolozsvár in Hungary
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
(now Cluj-Napoca
Cluj-Napoca
Cluj-Napoca , commonly known as Cluj, is the fourth most populous city in Romania and the seat of Cluj County in the northwestern part of the country. Geographically, it is roughly equidistant from Bucharest , Budapest and Belgrade...
in Romania
Romania
Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...
). In 1911 Fejér was appointed to the chair of mathematics at the University of Budapest and he held that post until his death. He was elected corresponding member (1908), member (1930) of the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
.
During his period in the chair at Budapest Fejér led a highly successful Hungarian school of analysis. He was the thesis advisor of mathematicians such as John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
, Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, George Pólya
George Pólya
George Pólya was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory...
and Pál Turán
Pál Turán
Paul Turán was a Hungarian mathematician who worked primarily in number theory. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers.- Life and education :...
.
Lipót Fejér is buried in Kerepesi Cemetery
Kerepesi Cemetery
Kerepesi Cemetery is the most famous cemetery in Budapest...
in Budapest.
Fejér's research concentrated on harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
and, in particular, Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
.
Fejér collaborated to produce important papers, one with Carathéodory
Constantin Carathéodory
Constantin Carathéodory was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory...
on entire function
Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane...
s in 1907 and another major work with Frigyes Riesz
Frigyes Riesz
Frigyes Riesz was a mathematician who was born in Győr, Hungary and died in Budapest, Hungary. He was rector and professor at University of Szeged...
in 1922 on conformal map
Conformal map
In mathematics, a conformal map is a function which preserves angles. In the most common case the function is between domains in the complex plane.More formally, a map,...
pings (specifically, a short proof of the Riemann mapping theorem).
Pólya on Fejer
Pólya writes the following about Fejér, telling us much about his personality:
He had artistic tastes. He deeply loved music and was a good pianist. He liked a well-turned phrase. 'As to earning a living', he said, 'a professor's salary is a necessary, but not sufficient, condition.' Once he was very angry with a colleague who happened to be a topologistTopologyTopology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, and explaining the case at length he wound up by declaring '... and what he is saying is a topological mapping of the truth'.
He had a quick eye for foibles and miseries; in seemingly dull situations he noticed points that were unexpectedly funny or unexpectedly pathetic. He carefully cultivated his talent of raconteur; when he told, with his characteristic gestures, of the little shortcomings of a certain great mathematician, he was irresistible. The hours spent in continental coffee houses with Fejér discussing mathematics and telling stories are a cherished recollection for many of us. Fejér presented his mathematical remarks with the same verve as his stories, and this may have helped him in winning the lasting interest of so many younger men in his problems.
In the same article Pólya writes about Fejér's style of mathematics:
Fejér talked about a paper he was about to write up. 'When I write a paper,' he said, 'I have to rederive for myself the rules of differentiation and sometimes even the commutative law of multiplication.' These words stuck in my memory and years later I came to think that they expressed an essential aspect of Fejér's mathematical talent; his love for the intuitively clear detail.
It was not given to him to solve very difficult problems or to build vast conceptual structures. Yet he could perceive the significance, the beauty, and the promise of a rather concrete not too large problem, foresee the possibility of a solution and work at it with intensity. And, when he had found the solution, he kept on working at it with loving care, till each detail became fully transparent.
It is due to such care spent on the elaboration of the solution that Fejér's papers are very clearly written, and easy to read and most of his proofs appear very clear and simple. Yet only the very naive may think that it is easy to write a paper that is easy to read, or that it is a simple thing to point out a significant problem that is capable of a simple solution.
External links
- Gabor Szegö Leopold Fejér: In memoriam, 1880-1959 Bull. Amer. Math. Soc. 66, 346-352 (1960).
- Birthplace of Lipót Fejér.