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- W4291290648 abstract "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 $N$ exponential polynomials implies approximate sum rules of order $N$; ii) generation of $N$ exponential polynomials implies approximate sum rules of order $N$, under the additional assumption of asymptotical similarity and reproduction of one exponential polynomial; iii) reproduction of an $N$-dimensional space of exponential polynomials and asymptotical similarity imply approximation order $N$; 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." @default.
- W4291290648 created "2022-08-14" @default.
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- W4291290648 date "2014-11-08" @default.
- W4291290648 modified "2023-10-16" @default.
- W4291290648 title "Approximation order and approximate sum rules in subdivision" @default.
- W4291290648 doi "https://doi.org/10.48550/arxiv.1411.2114" @default.
- W4291290648 hasPublicationYear "2014" @default.
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