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Fejér's main work was in harmonic analysis working on Fourier series and their singularities.
Fejér was born Leopold Weiss but changed his name around 1900 to make himself more Hungarian.
In 1897 Fejér won a prize in one of the first mathematics competitions to be held in Hungary. From that year until 1902 Fejér studied mathematics and physics at the University of Budapest and at the University of Berlin where he was a student of Schwarz. After changing his name from Weiss to Fejér, Schwarz refused to talk to him!
In 1900 Fejér published a fundamental summation theorem for Fourier series. This work was the basis of his doctoral thesis which he presented to the University of Budapest in 1902.
From 1902 to 1905 Fejér taught at the University of Budapest and from 1905 until 1911 he taught at Kolozsvár in Hungary (now Cluj in Romania). In 1911 Fejér was appointed to the char of mathematics at the University of Budapest and he held that post until his death. During his period in the chair at Budapest he led a highly successful Hungarian school of analysis.
Fejér's main work was in harmonic analysis. He worked on power series and on potential theory. Much of his work is on Fourier series and their singularities but he also contributed to approximation theory.
Fejér collaborated to produce important papers, one with Carathéodory on entire functions in 1907 and another major work with Riesz in 1922 on conformal mappings.
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