Guy David (mathematician)

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Guy RP David (born June 1, 1957 in Saint-Omer ) is a French mathematician who specializes in calculus.

David studied at the École normal supérieure in 1976 , received the Agrégation and the DEA and received his doctorate in 1981 from the University of Paris-Süd (Paris XI) under Yves Meyer (Thèse du 3ème cycle). The second part of the doctorate (Thèse d'État) took place in 1986 with Meyer ( Noyau de Cauchy et opérateurs de Caldéron-Zygmund ). From 1982 to 1989 he did research for the CNRS at the École Polytechnique . He has been a professor at the University of Paris-South since 1989 (from 1991 professor 1st class and from 2001 Classe exceptionelle).

David dealt with the theory of singular integral equations according to the theory of Alberto Calderón and with Hardy spaces . Among other things, he dealt with the problem of Painlevé , whose solution by Xavier Tolsa was also based on methods of David. David solved a special case in 1998, the Vitushkin conjecture . With Jean-Lin Journé in 1984 he proved the T (1) theorem, for which they received the Salem Prize . The theorem is of fundamental importance for the theory of singular integral operators of the Calderon-Zygmund type. He also dealt with the presumption of David Mumford and Shah (from the theory of image decomposition) and his contributions to the theory of Hardy spaces contributed to the solution of the continuous (analytical) version of the problem of the traveling salesman by Peter Jones in 1990. He worked with Stephen Semmes , with whom he published several books.

In 2004 he received the Prix ​​Servant and in 1990 the Prix IBM France. In the same year he received the Ferran Sunyer i Balaguer Prize for his book Singular sets of minimizers for the Mumford-Shah functional . From 1996 to 2001 he was a junior member and from 2010 to 2015 a senior member of the Institut Universitaire de France.

In 1986 he was invited to speak at the International Congress of Mathematicians in Berkeley (Opérateurs de Caldéron-Zygmund). In 1999 he was elected to the American Academy of Arts and Sciences .

Fonts

Books:

  • with Stephen Semmes: Analysis of and on uniformly rectifiable sets, Mathematical Surveys and Monographs 38. American Mathematical Society, Providence, RI, 1993.
  • with Stephen Semmes: Uniform rectifiability and quasiminimizing sets of arbitrary codimension, Memoirs AMS 2000
  • with Stephen Semmes: Singular integrals and rectifiable sets in Rn: au-delà des graphes lipschitziens, Astérisque 193, 1991
  • with Stephen Semmes: Fractured fractals and broken dreams. Self-similar geometry through metric and measure, Oxford Lecture Series in Mathematics and its Applications 7, Clarendon Press, Oxford 1997
  • with Alexis Bonnet, Cracktip is a global Mumford-Shah minimizer, Astérisque 274, 2001
  • Wavelets and singular integrals on curves and surfaces, Lecture notes in mathematics 1465, Springer 1991
  • Singular sets of minimizers for the Mumford-Shah functional, Progress in Mathematics, Birkhäuser 2005
  • with Tatiana Toro : Reifenberg parameterizations for sets with holes, Memoirs of the AMS 215, 2012

Some essays:

  • Courbes corde-arc et espaces de Hardy généralisés, Ann. Inst. Fourier (Grenoble), Vol. 32, 1982, pp. 227-239
  • Opérateurs intégraux singuliers sur certaines courbes du plan complexe , Ann. Sci. Ecole Norm. Sup. (4), Vol. 17, 1984, pp. 157-189.
  • with Ronald Coifman , Yves Meyer: La solution des conjectures de Calderón , Adv.in Math., Volume 48, 1983, pp. 144-148.
  • Morceaux de graphes lipschitziens et intégrales singulières sur une surface, Rev. Mat. Iberoamericana, Volume 4, 1988, pp. 73-114.
  • with JL Journé, S. Semmes: Opérateurs de Calderon-Zygmund, fonctions para-accrétives et interpolation , Rev. Mat. Iberoamericana, Volume 1, 1985, pp. 1-56.
  • with Jean-Lin Journé: A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2), Vol. 120, 1984, pp. 371-397
  • arcs for minimizers of the Mumford-Shah functional, SIAM J. Appl. Math., Vol. 56, 1996, pp. 783-888
  • Unrectifiable 1-sets have vanishing analytic capacity, Rev. Mat. Iberoamericana, Volume 14, 1998, pp. 369-479
  • with Pertti Mattila: Removable sets for Lipschitz harmonic functions in the plane, Rev. Mat. Iberoamericana, Volume 16, 2000, pp. 137-215
  • Should we solve Plateau's problem again? , in: Charles Fefferman, Alexandru D. Ionescu, DH Phong, Stephen Wainger (Eds.), Advances in Analysis: The Legacy of Elias M. Stein, Princeton University Press 2014, pp. 108–145.
  • with Tatiana Toro: Regularity of almost minimizers with free boundary, Calculus of Variations and Partial Differential Equations, Volume 54, 2015, 455-524, Arxiv
  • Local regularity properties of almost- and quasiminimal sets with a sliding boundary condition, Arxiv, 2014
  • with M. Filoche, D. Jerison, S. Mayboroda: A free boundary problem for the localization of eigenfunctions, Arxiv 2014

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ David Unrectifiable 1-sets have vanishing analytic capacity , Rev. Math. Iberoam. 14 (1998) 269-479
  3. ^ David, Journé: A boundedness criterion for generalized Calderón-Zygmund operators, Annals of Mathematics. Second Series, Volume 120, 1984, pp. 371-397
  4. ↑ Book of Members 1780 – present, Chapter D. (PDF; 575 kB) In: American Academy of Arts and Sciences (amacad.org). Retrieved February 24, 2018 .
personal data
SURNAME David, Guy
ALTERNATIVE NAMES David, Guy RP
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH June 1, 1957
PLACE OF BIRTH Saint-Omer