کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4606827 | 1631403 | 2016 | 22 صفحه PDF | دانلود رایگان |
Several properties of stationary subdivision schemes are nowadays well understood. In particular, it is known that the polynomial generation and reproduction capability of a stationary subdivision scheme is strongly connected with sum rules, its convergence, smoothness and approximation order. The aim of this paper is to show that, in the non-stationary case, exponential polynomials and approximate sum rules play an analogous role of polynomials and sum rules in the stationary case. Indeed, in the non-stationary univariate case we are able to show the following important facts: (i) reproduction of NN exponential polynomials implies approximate sum rules of order NN; (ii) generation of NN exponential polynomials implies approximate sum rules of order NN, under the additional assumption of asymptotical similarity and reproduction of one exponential polynomial; (iii) reproduction of an NN-dimensional space of exponential polynomials and asymptotical similarity imply approximation order NN; (iv) the sequence of basic limit functions of a non-stationary scheme reproducing one exponential polynomial converges uniformly to the basic limit function of the asymptotically similar stationary scheme.
Journal: Journal of Approximation Theory - Volume 207, July 2016, Pages 380–401