王新觉,檀结庆.Said型广义Ball基函数的拓展[J].数学研究及应用,2018,38(6):609~622
Said型广义Ball基函数的拓展
An Extension to the Said-Type Generalized Ball Basis Functions
投稿时间:2018-05-02  修订日期:2018-09-01
DOI:10.3770/j.issn:2095-2651.2018.06.007
中文关键词:  广义Ball基  对偶泛函  类Marsden恒等式  积分性质
英文关键词:generalized Ball basis  dual functionals  Marsden-like identity  integral property
基金项目:国家自然科学基金 (Grant No.61472466).
作者单位
王新觉 西北工业大学航海学院, 陕西 西安710072 
檀结庆 合肥工业大学数学学院, 安徽 合肥 230009 
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中文摘要:
      在本文中,我们给出了构造Said型广义Ball基函数的新方法,该方法的优点在于,既可以推出奇次多项式的Said型广义Ball基函数表示,也可以推出偶次多项式的Said型广义Ball基函数表示;该方法的另一优点是,能很自然地定义Said型广义Ball基函数的对偶泛函; 给出了Said型广义Ball基函数的积分性质;定义了一种新的基函数, Said型广义Ball基函数是其特例; 给出了这种新的基函数的对偶泛函和类Marsden恒等式.
英文摘要:
      In this paper, we present a general approach to the construction of the Said-type generalized Ball basis functions. The advantage of our approach lies in the fact that it can be used to derive the expressions for polynomials of not only odd degrees but also even degrees in terms of the Said-type generalized Ball basis functions. We then define dual functionals for the Said-type generalized Ball basis in a very natural manner and bring to light the integral property of the Said-type generalized Ball basis functions. Last but not least, new polynomial basis functions are defined which include the Said-type generalized Ball basis functions as their special case, and the corresponding dual functionals and Marsden-like identity are obtained.
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