Fejer's Theorem states that the Cesaro means, meaning the running averages of the first several partial sums, of the Fourier series of any continuous periodic function converge uniformly to that function, even in cases where the Fourier series's own partial sums fail to converge at every point. Named for Lipot Fejer, who proved it in 1900 while still a student, it supplied a better-behaved substitute for ordinary Fourier series convergence and remains a foundational result of Fourier analysis.
Facts
Partially Attested
Proof YearSource gives the date Fejer submitted the result to the Paris Academy of Sciences, not an explicit proof year. StatementFor a continuous function f with period 2 pi, the Cesaro means of the partial sums of its Fourier series converge uniformly to f on the real line. 1 Classification
Statement Form Connections
Sources
1. Fejer's theorem (Wikipedia)
Theorem statement, final sentenceQuote, Theorem statement, final sentence
converges uniformly to f on R as n tends to infinity
2. Lipot Fejer (MacTutor History of Mathematics)
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