Monomial-Curve Criterion for Real Analyticity
A test for whether an arc-analytic function with subanalytic graph is real analytic at a point, using only its restrictions to monomial curves t goes to (t^m1, ..., t^mn). The function is analytic at the origin exactly when each such restriction lands in the subring of power series generated by those monomial powers, a condition amounting to the vanishing of finitely many Taylor coefficients bounded by the Frobenius number of the exponents. Sharpens the binomial-curve criterion of Kucharz and Kurdyka and is proved by monomial principalization.
Real analytic functions and monomial curves
Janos Kollar, arXiv 2304.01338v1, math.CA and math.AG, April 2023, no journal reference. The paper gives a criterion for real analyticity at a point in terms of restrictions to a very sparse family o…