HYPERBOLICITY WITH WEIGHT OF POLYNOMIALS IN TERMS OF COMPARING THEIR POWER

Abstract

For a given completely regular Newton polyhedron R, and a given vector N is an element of R-n, we give conditions under which a weakly hyperbolic polynomial (with respect to the vector N) P(xi) = P(xi(1), ..., xi(n)) is R-hyperbolic (with respect to the vector N). For polynomials of two variables, the largest number s > 0 is determined for which an R-hyperbolic (with respect to the vector N) polynomial is s -hyperbolic.