Spaces of generalized splines over T-meshes

We consider a class of non-polynomial spline spaces over T-meshes, that is, of spaces locally spanned both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such spaces, we provide, under certain conditions, a dimension formula and a basis based on the notion of minimal determining set. We explicitly examine some relevant cases, which enjoy a noteworthy behaviour with respect to differentiation and integration; finally, we also study the approximation power of the just constructed spline spaces.