Reconstruction of algebraic sets from dynamic moments

Gabriela Putinar; Mihai Putinar

Displaying similar documents to “Reconstruction of algebraic sets from dynamic moments”

On the polynomial-like behaviour of certain algebraic functions

Charles Feffermann, Raghavan Narasimhan (1994)

Annales de l'institut Fourier

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Given integers $D > 0, n > 1, 0 < r < n$ and a constant $C > 0$ , consider the space of $r$ -tuples $\vec{P} = (P_{1} ... P_{r})$ of real polynomials in $n$ variables of degree $\leq D$ , whose coefficients are $\leq C$ in absolute value, and satisfying $\det {(\frac{\partial P_{i}}{\partial x_{i}} (0))}_{1 \leq i, j \leq r} = 1$ . We study the family ${f | V}$ of algebraic functions, where $f$ is a polynomial, and $V = {| x | \leq δ, \vec{P} (x) = 0}, δ > 0$ being a constant depending only on $n, D, C$ . The main result is a quantitative extension theorem for these functions which is uniform in $\vec{P}$ . This is used to prove Bernstein-type inequalities which are again uniform with respect to $\vec{P}$ . ...

On algebraic solutions of algebraic Pfaff equations

Henryk Żołądek (1995)

Studia Mathematica

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We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system $ẋ = z^{s}, ẏ = x^{s}, ż = y^{s}$ . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.