Idéaux de fonctions différentiables. II

Tougeron, Jean-Claude; Merrien, Jean

doi:10.5802/aif.341

Cited by 99 publications

(28 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To trace the history of the problem the reader may consult [4,5,8,10]. The main results, Theorems 1.1, 1.8, 1.9 and Corollary 1.7, are new and considerably stronger than the ones previously known.…”

mentioning

confidence: 97%

Power series and smooth functions equivalent to a polynomial

Kucharz¹

1986

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. An algebraic criterion is given for a power series in n variables over a field of characteristic 0 to be equivalent to a polynomial in n -k variables over the ring of power series in k variables. For convergent power series over the reals or complexes a geometric interpretation of the criterion is established. An analogous sufficient condition is obtained for germs of smooth functions. Most of the previously known results follow easily from the criterion.

show abstract