Bivariate Hermite–Birkhoff polynomial interpolation with asymptotic conditions

Some asymptotic conditions along prescribed directions are added to the usual interpolation data in bivariate problems. These asymptotic conditions are written in terms of interpolation and then the new problem is studied in the frame of the interpolation systems introduced by Gasca and Maeztu some years ago. A Newton type interpolation formula is obtained for the enlarged problem and then some particular cases are studied.