In mathematics, Dini's criterion is a condition for the pointwise convergence of Fourier series, introduced by Ulisse Dini (1880). == Statement == Dini's criterion states that if a periodic function f {\displaystyle f} has the property that ( f ( t ) + f ( − t ) ) / t {\displaystyle (f(t)+f(-t))/t} is locally integrable near 0 {\displaystyle 0} , then the Fourier series of f {\displaystyle f} converges to 0 {\displaystyle 0} at t = 0 {\displaystyle t=0} .
In mathematics, Dini's criterion is a condition for the pointwise convergence of Fourier series, introduced by Ulisse Dini (1880). == Statement == Dini's criterion states that if a periodic function f {\displaystyle f} has the property that ( f ( t ) + f ( − t ) ) / t {\displaystyle (f(t)+f(-t))/t} is locally integrable near 0 {\displaystyle 0} , then the Fourier series of f {\displaystyle f} converges to 0 {\displaystyle 0} at t = 0 {\displaystyle t=0} .
Source: Wikipedia "Dini criterion" · CC BY-SA 4.0
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