Louis Boutet de Monvel

from Wikipedia, the free encyclopedia

Louis Boutet de Monvel (born June 22, 1941 - † December 25, 2014 ) was a French mathematician who dealt with functional analysis and micro-local analysis with applications to partial differential equations and mathematical physics.

Boutet de Monvel studied from 1960 at the École normal supérieure (ENS) and received his doctorate in 1969 with Laurent Schwartz in Paris . From 1967 to 1969 he taught in Algiers and from 1969 to 1971 he was professor at the University of Nice , 1971 to 1975 at the University of Paris VII and 1975 to 1979 at the University of Grenoble . He was then a professor at the University of Paris VI Pierre and Marie Curie and headed the Center de mathématiques of the ENS from 1978 to 1985.

Boutet de Monvel developed an algebra of pseudo differential operators in boundary value problems or on manifolds with boundaries . He also dealt with Toeplitz operators, which have a symbolic calculus (a special case of C * algebra ) similar to that of pseudo differential operators. They are used in deformation quantization, which was also investigated by Monvel (he wrote about it in the book "Toeplitz operators and deformation algebras"). He also dealt with Bergman kernels in complex analysis (collaboration with Johannes Sjöstrand ).

In 2007 he received the Émile Picard Medal of the French Academy of Sciences and in 2003 its Prix fondé par l'État. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice (Une algèbre associées auxproblemèmes aux limites elliptiques) . In 2012 he was elected to the American Academy of Arts and Sciences .

From 1971 to 1991 he was a member of Nicolas Bourbaki . 1979–1983 he was co-editor of the Mathematische Annalen .

Philibert Nang and Gilles Lebeau are among his PhD students .

Fonts

  • with Paul Krée: Pseudo-differential operators and Gevrey classes. In: Annales de l'Institut Fourier. Volume 17, No. 1, 1967, pp. 295-323, ( online ).
  • Hypoelliptic operators with double characteristics and related pseudo-differential operators. In: Communications on Pure and Applied Mathematics. Volume 27, No. 5, 1974, pp. 585-639, doi : 10.1002 / cpa . 3160270502 .
  • with François Treves : On a Class of Pseudodifferential Operators with Double Characteristics. In: Inventiones Mathematicae . Volume 24, No. 1, 1974, pp. 1-34 .
  • with Alain Grigis, Bernard Helffer : Paramétrixes d'opérateurs pseudo-différentiels a caractéristiques multiples. In: Journées Equations aux Dérivées Partielles. 1975 = Astérisque. Volume 34/35, 1976, pp. 93-121, ( online ).
  • with Johannes Sjöstrand : Sur la singularité des noyaux de Bergman et de Szegö. In: Journées Equations aux Dérivées Partielles. 1975 = Astérisque. Volume 34/35, 1976, pp. 123-164, ( online ).
  • with Victor Guillemin : The spectral theory of Toeplitz Operators (= Annals of Mathematics Studies. 99). Princeton University Press et al., Princeton NJ et al. 1981, ISBN 0-691-08284-7 .

Web links

References

  1. ^ Boutet de Monvel: Boundary problems for pseudodifferential operators. In: Acta Mathematica . Volume 126, 1971, pp. 11-51, doi : 10.1007 / BF02392024 .
  2. ↑ They can be defined with the help of Toeplitz matrices , in which the matrix elements are the same in every diagonal.
  3. ↑ 1978 by Moshé Flato , Sternheimer, Fronsdal and André Lichnerowicz introduced by analogy of the correspondence of Poisson brackets to commutators in the transition from classical mechanics to quantum mechanics by Paul Dirac
personal data
SURNAME Boutet de Monvel, Louis
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH June 22, 1941
DATE OF DEATH December 25, 2014