Composite differentiable functions
Copyright policy )Composite differentiable functions
We introduce a new point of view towards Glaeser's theorem on composite $C^\infty$ functions [Ann. of Math. 1963], with respect to which we can formulate a ``$C^k$ composite function property" that is satisfied by all semiproper real analytic mappings. As a consequence, we see that a closed subanalytic set $X$ satisfies the $C^\infty$ composite function property if and only if the ring $C^\infty (X)$ of $C^\infty$ functions on $X$ is the intersection of all finite differentiability classes.
19 pages, hard copy available on request. amstex v 2
real analytic mapping, \(C^ \infty\) composition function property, 58C25, Analytic algebras and generalizations, preparation theorems, 32B20, Mathematics - Algebraic Geometry, 32K15, 32B20, 58C27 (Primary) 32K15, 58C25 (Secondary), FOS: Mathematics, \(C^\infty\)-functions, quasi-analytic functions, Semi-analytic sets, subanalytic sets, and generalizations, Algebraic Geometry (math.AG)
real analytic mapping, \(C^ \infty\) composition function property, 58C25, Analytic algebras and generalizations, preparation theorems, 32B20, Mathematics - Algebraic Geometry, 32K15, 32B20, 58C27 (Primary) 32K15, 58C25 (Secondary), FOS: Mathematics, \(C^\infty\)-functions, quasi-analytic functions, Semi-analytic sets, subanalytic sets, and generalizations, Algebraic Geometry (math.AG)
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