Behaviour Preserving Extensions of Univariate and Bivariate Functions

Given function values on a domain $D_0$, possibly with noise, we examine the possibility of extending the function to a larger domain $D$, $D_0\subset D$. In addition to smoothness at the boundary of $D_0$, the extension on $D\setminus D_0$ should also inherit behavioral trends of the function on $D_0$, such as growth and decay or even oscillations. The approach chosen here is based upon the framework of linear models, univariate or bivariate, with constant or varying coefficients.