On interpolation

MEAN VALUE INTERPOLATION ON SPHERES

In this paper we consider   multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have   concentric spheres. Indeed, we consider the problem in three variables when it is not correct.  

On Equational Craig Interpolation

Generalizations of Craig interpolation are investigated for equational logic. Our approach is to do as much as possible at a categorical level, before drawing out the concrete implications.

On Polyharmonic Interpolation

In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from C∞ or analytic functions in the ball BR. We prove two main results on the interpolation of C∞ or analytic functions f in the ball BR by polyharmonic functions h of a given...

On partial polynomial interpolation

The Alexander-Hirschowitz theorem says that a general collection of k double points in P imposes independent conditions on homogeneous polynomials of degree d with a well known list of exceptions. We generalize this theorem to arbitrary zero-dimensional schemes contained in a general union of double points. We work in the polynomial interpolation setting. In this framework our main result says ...

Notes on Interpolation Inequalities