Some properties of LR-splines

• A polynomial representation formula for the LR B-spline collection is shown.
• The number of functions of the LR B-spline collection whose support contains a point is studied.
• The close relation between the above properties is asserted.

Recently a new approach to piecewise polynomial spaces generated by B-spline has been presented by T. Dokken, T. Lyche and H.F. Pettersen, namely Locally Refined splines. In their recent work (Dokken et al., 2013) they define the LR B-spline collection and provide tools to compute the space dimension. Here different properties of the LR-splines are analyzed: in particular the coefficients for polynomial representations and their relation with other properties such as linear independence and the number of B-splines covering each element.