On the real algebra of quasianalytic function germs

  title={On the real algebra of quasianalytic function germs},
  author={Krzysztof Jan Nowak},
Given a quasianalytic system Q = (Qn)n∈N of sheaves, denote by Qn the local ring of Q-analytic function germs at 0 ∈ Rn. This paper introduces the concepts of Lojasiewicz radical and geometric spectrum SpegQn ⊂ SperQn. Via the Lojasiewicz inequality, a version of the Nullstellensatz for Qn is given. We establish a quasianalytic version of the Artin–Lang property for Qn. Finally, we prove, by means of transformation to normal crossings by blowing up, that the Lojasiewicz radical £(I) of any… CONTINUE READING