| Abstract: | The paper presents a simple procedure for the construction of quasi-interpolation operators in spaces of m-harmonic splines in Rd, which reproduce polynomials of high degree. The procedure starts from a generator ?0, which is easy to derive but with corresponding quasi-interpolation operator reproducing only linear polynomials, and recursively defines generators ?1,?2,…,?m−1 with corresponding quasi-interpolation operators reproducing polynomials of degree up to 3,5,…,2m−1 respectively. The construction of ?j from ?j−1 is explicit, simple and independent of m. The special case d=1 and the special cases d=2,m=2,3,4 are discussed in details. |
