Bivariate Polynomial Interpolation with Asymptotic Conditions

Bivariate Hermite-Birkhoff interpolation problems with an asymptotic condition on some Straight lines are studied, using a Newton approach. The existence and uniqueness of solution in an adequate polynomial space is proved. Special attention is paid to the case of vanishing asymptotic conditions, which allows us to describe by a characteristic property the interpolation space when there is no asymptotic condition.