Marc-Antoine Parseval
Encyclopedia
Marc-Antoine Parseval des Chênes (April 27, 1755 – August 16, 1836) was a French
mathematician
, most famous for what is now known as Parseval's theorem
, which presaged the unitarity
of the Fourier transform
.
He was born in Rosières-aux-Salines
, in France
, into an aristocratic French family, and married Ursule Guerillot in 1795, but divorced her soon thereafter. A monarchist opposed to the French revolution
, imprisoned in 1792, Parseval fled the country later for publishing poetry critical of the government of Napoleon
.
Later, he was nominated to the French Academy of Sciences
five times, from 1796 to 1828, but was never elected. His only mathematical publications were, apparently, five papers, published in 1806 as Mémoires présentés à l'Institut des Sciences, Lettres et Arts, par divers savants, et lus dans ses assemblées. Sciences mathématiques et physiques. (Savants étrangers.) This combined the following earlier monographs:
It was in the second, 1799, memoir in which he stated, but did not prove (claiming it to be self-evident), the theorem that now bears his name. He further expanded upon it in his 1801 memoir, and used it to solve various differential equation
s. The theorem was first printed in 1800 as a part (p. 377) of Traité des différences et des séries by Lacroix.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, most famous for what is now known as Parseval's theorem
Parseval's theorem
In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum of the square of a function is equal to the sum of the square of its transform. It originates from a 1799 theorem about series by Marc-Antoine Parseval, which was later...
, which presaged the unitarity
Unitary operator
In functional analysis, a branch of mathematics, a unitary operator is a bounded linear operator U : H → H on a Hilbert space H satisfyingU^*U=UU^*=I...
of the Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
.
He was born in Rosières-aux-Salines
Rosières-aux-Salines
Rosières-aux-Salines is a commune in the Meurthe-et-Moselle département in north-eastern France.In the past, inhabitants of Rosières-aux-Salines were insultingly known by their neighbours as oua-oua , on account of a speech defect caused by a local thyroid condition, which was considered hilarious....
, in France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, into an aristocratic French family, and married Ursule Guerillot in 1795, but divorced her soon thereafter. A monarchist opposed to the French revolution
French Revolution
The French Revolution , sometimes distinguished as the 'Great French Revolution' , was a period of radical social and political upheaval in France and Europe. The absolute monarchy that had ruled France for centuries collapsed in three years...
, imprisoned in 1792, Parseval fled the country later for publishing poetry critical of the government of Napoleon
Napoleon I of France
Napoleon Bonaparte was a French military and political leader during the latter stages of the French Revolution.As Napoleon I, he was Emperor of the French from 1804 to 1815...
.
Later, he was nominated to the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
five times, from 1796 to 1828, but was never elected. His only mathematical publications were, apparently, five papers, published in 1806 as Mémoires présentés à l'Institut des Sciences, Lettres et Arts, par divers savants, et lus dans ses assemblées. Sciences mathématiques et physiques. (Savants étrangers.) This combined the following earlier monographs:
- "Mémoire sur la résolution des équations aux différences partielles linéaires du second ordre," (May 5, 1798).
- "Mémoire sur les séries et sur l'intégration complète d'une équation aux différences partielles linéaires du second ordre, à coefficents constants," (April 5, 1799).
- "Intégration générale et complète des équations de la propagation du son, l'air étant considéré avec ses trois dimensions," (July 5, 1801).
- "Intégration générale et complète de deux équations importantes dans la mécanique des fluides," (August 16, 1803).
- "Méthode générale pour sommer, par le moyen des intégrales définies, la suite donnée par le théorème de M. Lagrange, au moyen de laquelle il trouve une valeur qui satisfait à une équation algébrique ou transcendante," (May 7, 1804).
It was in the second, 1799, memoir in which he stated, but did not prove (claiming it to be self-evident), the theorem that now bears his name. He further expanded upon it in his 1801 memoir, and used it to solve various differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s. The theorem was first printed in 1800 as a part (p. 377) of Traité des différences et des séries by Lacroix.