Born: March 5, 1915, Paris [Died] July 4, 2002. Paris. French mathematician. Studied at the Ecole Normale Supérieure and the University of Paris. After receiving his doctorate in mathematics in Paris, he was professor at the University of Nancy from 1945 to 1952, and at the Ecole Polytechnique from 1959 to 1960 and 1963 to 1983. In 1950, at the International Congress of Mathematicians held in Cambridge, USA, he was awarded the Fields Medal for his theory of generalization of the concept of function called distribution. Before Schwartz, physicists had worked with Paul Dirac's delta function, a density distribution whose value is always 0 for x ≠ 0, infinity for x = 0, and its integral over the whole number line is 1. Schwartz established the theory of distributions by using a method of functional analysis to formulate such generalized functions as elements of the dual space of the space of all smooth functions with compact support. Schwarz's theory of generalized functions was subsequently applied to partial differential equations, potential theory, and spectral theory. Schwartz |
[生]1915.3.5. パリ [没]2002.7.4. パリ フランスの数学者。エコール・ノルマル・シュペリュールとパリ大学に学ぶ。パリで数学の博士号を取得したのち,1945~52年ナンシー大学,1959~60年および 1963~83年エコール・ポリテクニクで教授を務めた。1950年,アメリカ合衆国のケンブリッジで開催された国際数学者会議で,超関数と呼ばれる関数概念の一般化の理論により,フィールズ賞を受賞した。シュワルツ以前にも,物理学者はポール・ディラックのδ関数と呼ばれる密度分布を扱ってきた。δ関数は x≠0 のとき値が常に 0で,x=0 で無限大となり,数直線全体での積分値が 1になるという性質をもつ。シュワルツはコンパクトな台をもつ,なめらかな関数全体の空間の双対空間の要素として,このような一般化された関数を定式化する関数解析の手法により,超関数の理論を確立した。シュワルツの超関数の理論はその後,偏微分方程式,ポテンシャル論,スペクトル理論などに応用された。 シュワルツ
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