Joint continuity of division of smooth functions. I: Uniform lojasiewicz estimates

Mark Alan Mostow, Steven Shnider

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7 Scopus citations


In this paper we study the question of the existence of a continuous inverse to the multiplication mapping (formula presented) defined on pairs of C00 functions on a manifold M. Obviously, restrictions must be imposed on the domain of such an inverse. This leads us to the study of a modified problem: Find an appropriate domain for the inverse of (formula presented) mapping of the manifold M into an analytic manifold N and p is a fixed analytic function on N. We prove a theorem adequate for application to the study of inverting the mapping (formula presented), where A is a vector valued C function and A is a square matrix valued C00 function on M whose determinant may vanish on a nowhere dense set.

Original languageEnglish
Pages (from-to)573-583
Number of pages11
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - Dec 1985
Externally publishedYes


  • Continuity of division
  • Continuous dependence of solutions on parameters
  • Division of distributions
  • Division of smooth functions
  • Function spaces
  • Mather Division Theorem
  • Matrix equations


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