An Extension to the Said-Type Generalized Ball Basis Functions

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.