Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials

作者：Cheng, Ting; Yang, Xiaoyuan^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, 2016(1): 166.

DOI：10.1186/s13660-016-1106-0

• refinable functions
• generalized Bernstein polynomials
• cascade algorithms
• Riesz wavelet bases

In this paper, we construct a new family of refinable functions from generalized Bernstein polynomials, which include pseudo-splines of Type II. A comprehensive analysis of the refinable functions is carried out. We then prove the convergence of cascade algorithms associated with the new masks and construct Riesz wavelets whose dilation and translation form a Riesz basis for L-2(R). Stability of the subdivision schemes, regularity and approximation orders are obtained. We also illustrate the symmetry of the corresponding refinable functions.

• 出版日期2016-6-24
• 单位北京航空航天大学