10 citations · 23 across the 9 of their papers we have counts for
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Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings
Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein +2
It is shown that Denjoy-Carleman quasi-analytic rings of germs of functions in two or more variables fail to satisfy the Weierstrass Preparation Theorem. The result is proven via a…
A Nullstellensatz for Łojasiewicz ideals
Francesca Acquistapace, Fabrizio Broglia, Andreea Nicoara
For an ideal of smooth functions that is either Łojasiewicz or weakly Łojasiewicz, we give a complete characterization of the ideal of functions vanishing on its variety in terms o…
On the Nullstellensätze for Stein spaces and -analytic sets
Francesca Acquistapace, Fabrizio Broglia, Jose F. Fernando
In this work we prove the real Nullstellensatz for the ring of analytic functions on a -analytic set in terms of the saturation of Łoja…