On the real algebra of Denjoy–Carleman classes

• Federica Pieroni ^[1]
  1. [1] University of Pisa

     University of Pisa

     Pisa, Italia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 2, 2007, págs. 321-351
• Idioma: inglés
• DOI: 10.1007/s00029-007-0039-3
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• Resumen

  • We show that a nonnegative function germ at the origin of R2R2 belonging to a quasianalytic Denjoy–Carleman class can be written as a sum of two squares of functions which lie in a Denjoy–Carleman class again. When the germ is elliptic we prove that the class is the same, in the general case a loss of regularity is possible. As a consequence we deduce the Artin–Lang property for suitable unions of such quasianalytic classes.