An Extension to the Said-Type Generalized Ball Basis Functions
Received:May 02, 2018  Revised:September 01, 2018
Key Word: generalized Ball basis   dual functionals   Marsden-like identity   integral property  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.61472466).
Author NameAffiliation
Xinjue WANG School of Marine Science and Technology, Northwestern Polytechnical University, Shaanxi 710072, P. R. China 
Jieqing TAN School of Mathematics, Hefei University of Technology, Anhui 230009, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2018.06.007
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