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Charles-Jean de la Vallée-Poussin (August 141866 - March 21962) was a Belgian mathematician.
Biography
He was born in Louvain, Belgium and remained there his whole life during. 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.
Work
Althought, 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
- <math> V_n=\frac{S_n+S_{n+1}+\ldots+S_{2n-1}}{n} <math>,
where
- <math> S_n=\frac{1}{2}c_0(f)+\sum_{i=1}^n c_i(f) T_i <math>
and
- <math> c_i(f) <math>
are the vectors of the dual basis with respect to the basis of Chebyshev polynomials (defined as
- <math> (T_0/2,T_1,\cdots,T_n) <math>).
Note that the formula is also valid with <math> S_n <math> being the Fourier sum of a <math> 2\pi<math>-periodic function 'F' such that
- <math> F(\theta)=f(\cos\theta)<math>.
Finally, the de la Vallée-Poussin sums can be evaluated in terms of the so-called Fejer sums (say <math>F_n<math>) : <math>V_n=2F_{2n-1}-F_{n-1}<math>.
Later, he worked on potential theory and complex analysis.
External links
- A biography (http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Vallee_Poussin.html)
- Obituary (http://www.numbertheory.org/obituaries/LMS/de_la_vallee_poussin/index.html)