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| [[Image:De La Vallée Poussin.jpg|thumb|right|Charles Levieux,<br>Baron de la Vallée Poussin]]
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| '''Charles-Jean Étienne Gustave Nicolas de la Vallée Poussin''' (14 August 1866 - 2 March 1962) was a [[Belgium|Belgian]] [[mathematician]]. He is most well known for proving the [[Prime number theorem]]. | |
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| The king of Belgium ennobled him with the title of baron. | |
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| ==Biography==
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| De la Vallée-Poussin was born in [[Leuven]], [[Belgium]]. He studied [[mathematics]] at the [[Catholic University of Leuven (1834–1968)|Catholic University of Leuven]] under his uncle Louis-Philippe Gilbert, after he had earned his [[bachelor's degree]] in [[engineering]]. De la Vallée-Poussin was encouraged to study for a doctorate in [[physics]] and mathematics, and in 1891, at the age of just 25, he became an [[assistant professor]] in mathematical analysis.
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| De la Vallée-Poussin became a professor at the same university (as was his father, [[Charles-Louis-Joseph-Xavier de la Vallée-Poussin]], who taught [[mineralogy]] and [[geology]]) in 1892. De la Vallée-Poussin was awarded with Gilbert's chair when Gilbert died. While he was a professor there, de la Vallée-Poussin carried out research in mathematical analysis and the theory of numbers, and in 1905 was awarded the Decennial Prize for Pure Mathematics 1894-1903. He was awarded this prize a second time in 1924 for his work during 1914 - 23.
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| In 1898, de la Vallée-Poussin was appointed as the correspondent to the [[Royal Belgian Academy of Sciences]], and he became a Member of the Academy in 1908. In 1923, he became the President of the Division of Sciences.
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| In August 1914, de la Vallée-Poussin escaped from Leuven at the time of its destruction by the invading [[German Army]] of [[World War I]], and he was invited to teach at [[Harvard University]] in the [[United States]]. He accepted this invitation. In 1918, de la Vallée-Poussin returned to Europe to accept professorships in [[Paris]] at the [[Collège de France]] and at [[the Sorbonne]].
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| After the war was over, de la Vallée-Poussin returned to Belgium, The International Union of Mathematicians was created, and he was invited to become its President. Between 1918 and 1925, de la Vallée-Poussin traveled extensively, lecturing in [[Geneva]], [[Strasbourg]], and [[Madrid]]. and then in the United States where he gave lectures at the Universities of Chicago, California, Pennsylvania, and Brown University, Yale University, Princeton University, Columbia University, and the Rice Institute of Houston.
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| De la Vallée-Poussin was given the titles of Doctor Honoris Causa of the Universities of Paris, Toronto, Strasbourg, and Oslo, an Associate of the Institute of France, and a Member of the [[Pontifical Academy of Sciences]],<ref>http://www.casinapioiv.va/content/accademia/en/academicians/deceased/delavalleepoussin.html</ref> Nazionale dei Lincei, Madrid, Naples, Boston. He was awarded the title of Baron by King Albert 1 of the Belgians in 1928.
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| In 1961, de la Vallée-Poussin fractured his shoulder, and this accident and its complications led to his death in [[Watermael-Boitsfort]], near [[Brussels, Belgium]], a few months later.
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| A student of his, [[Georges Lemaître]], was the first man to propose the [[Big Bang theory]] of the formation of the [[Universe]].
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| ==Work==
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| Although his first mathematical interests were in analysis, he became suddenly famous as he proved the [[prime number theorem]] independently of his coeval [[Jacques Hadamard]] in 1896.
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| Afterwards, he found interest in [[approximation theory]]. He defined, for any [[continuous function]] ''f'' on the standard [[Interval (mathematics)|interval]] [−1,1], the sums
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| :<math> V_n=\frac{S_n+S_{n+1}+\ldots+S_{2n-1}}{n} </math>,
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| where
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| :<math> S_n=\frac{1}{2}c_0(f)+\sum_{i=1}^n c_i(f) T_i </math>
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| and
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| :<math> c_i(f) \,</math>
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| are the vectors of the [[dual basis]] with respect to the [[polynomial basis|basis]] of [[Chebyshev polynomials]] (defined as
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| :<math> (T_0/2,T_1,\cdots,T_n) </math>. | |
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| Note that the formula is also valid with <math> S_n </math> being the [[Jean Baptiste Joseph Fourier|Fourier]] sum of a <math> 2\pi</math>-[[periodic function]] 'F' such that
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| :<math> F(\theta)=f(\cos\theta) \,</math>. | |
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| Finally, the de la Vallée-Poussin sums can be evaluated in terms of the so-called [[Lipót Fejér|Fejér]] sums (say <math>F_n</math>)
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| :<math>V_n=2F_{2n-1}-F_{n-1} \,</math>. | |
| The kernel is bounded (<math>V_n \le 3</math>) and obeys the property
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| :<math>f*V_n = f \,</math>, if <math>f(x)= \sum_{j=-n}^n a_j e^{i j x}. \,</math> | |
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| Later, he worked on [[potential theory]] and [[complex analysis]].
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| ==Notes==
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| {{Reflist}}
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| ==See also==
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| *[[La Vallée-Poussin]]
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| ==External links==
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| * Biographie Universelle, by [[Didot]].
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| * {{MacTutor Biography|id=Vallee_Poussin}}
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| * [http://www.numbertheory.org/obituaries/LMS/de_la_vallee_poussin/index.html Obituary]
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| {{Use dmy dates|date=September 2010}}
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| {{Authority control|VIAF=114895187}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = La Vallee-Poussin, Charles-Jean De
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = mathematician
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| | DATE OF BIRTH = 14 August 1866
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| | PLACE OF BIRTH = Leuven, Belgium
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| | DATE OF DEATH = 2 March 1962
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| | PLACE OF DEATH = Boitsfort, Belgium
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| }}
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| {{DEFAULTSORT:La Vallee-Poussin, Charles-Jean De}}
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| [[Category:1866 births]]
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| [[Category:1962 deaths]]
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| [[Category:People from Leuven]]
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| [[Category:19th-century mathematicians]]
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| [[Category:20th-century mathematicians]]
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| [[Category:Number theorists]]
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| [[Category:Harvard University faculty]]
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| [[Category:University of Paris faculty]]
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| [[Category:Belgian scientists]]
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| [[Category:Belgian mathematicians]]
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| [[Category:Catholic University of Leuven alumni (pre-1968)]]
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| [[Category:Barons of Belgium]]
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| [[Category:ICM 1897 Plenary and Invited Speakers]]
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