Displaying similar documents to “Some properties of solutions to polynomial systems of differential equations.”

Wold decomposition of the Hardy space and Blaschke products similar to a contraction

M. Stessin (1999)

Colloquium Mathematicae

Similarity:

The classical Wold decomposition theorem applied to the multiplication by an inner function leads to a special decomposition of the Hardy space. In this paper we obtain norm estimates for componentwise projections associated with this decomposition. An application to operators similar to a contraction is given.

Jung's type theorem for polynomial transformations of ℂ²

Sławomir Kołodziej (1991)

Annales Polonici Mathematici

Similarity:

We prove that among counterexamples to the Jacobian Conjecture, if there are any, we can find one of lowest degree, the coordinates of which have the form x m y n + terms of degree < m+n.

Factoring polynomials over global fields

Karim Belabas, Mark van Hoeij, Jürgen Klüners, Allan Steel (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field.