Charles Jean de la Vallée-Poussin

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Charles-Jean de la Vallée-Poussin (August 14, 1866 - March 2, 1962) was a Belgian mathematician.

[edit] Biography

He was born in Louvain, Belgium and remained there his whole life. He was taught mathematics at the Université catholique de Louvain by Louis-Philippe Gilbert, after he obtained his diploma in engineering. He became a teacher at the same university (just like his father who taught mineralogy and geology) in 1892, obtaining Gilbert's chair at his death. In 1961, he fractured his shoulder and this incident led him to death in Boitsfort, Brussels a couple of months later.

[edit] Work

Although, his first mathematical interests were in analysis, he became suddenly famous as he proved the prime number theorem independently of Jacques Hadamard in 1896.

Afterwards, he found interest in approximation theory. He defined, for any continuous function f on the standard interval [−1,1], the sums

V_n=\frac{S_n+S_{n+1}+\ldots+S_{2n-1}}{n},

where

S_n=\frac{1}{2}c_0(f)+\sum_{i=1}^n c_i(f) T_i

and

ci(f)

are the vectors of the dual basis with respect to the basis of Chebyshev polynomials (defined as

(T_0/2,T_1,\cdots,T_n)).

Note that the formula is also valid with Sn being the Fourier sum of a 2π-periodic function 'F' such that

F(θ) = f(cosθ).

Finally, the de la Vallée-Poussin sums can be evaluated in terms of the so-called Fejer sums (say Fn) : Vn = 2F2n − 1 − Fn − 1.

Later, he worked on potential theory and complex analysis.

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