Extensions of k-regulous functions from two-dimensional varieties

Abstract

We prove that a k-regulous function defined on a two-dimensional nonsingular affine variety can be extended to an ambient variety. Additionally we derive some results concerning sums of squares of k-regulous functions; in particular we show that every positive semi-definite regular function on a non-singular affine variety can be written as a sum of squares of locally Lipschitz regulous functions.