In this paper we focus on Hermite subdivision operators that act on vector valued data interpreting their components as function values and associated consecu- tive derivatives. We are mainly interested in studying the exponential and polynomial preservation capability of such kind of operators, which can be expressed in terms of a generalization of the spectral condition property in the spaces generated by polynomials and exponential functions. The main tool for our investigation are con- volution operators that annihilate the aforementioned spaces, which apparently is a general concept in the study of various types of subdivision operators. Based on these annihilators, we characterize the spectral condition in terms of factorization of the subdivision operator.
Factorization of Hermite subdivision operators preserving exponentials and polynomials / Conti, Costanza; Cotronei, Mariantonia; Sauer, Tomas. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - STAMPA. - 42:(2016), pp. 1055-1079. [10.1007/s10444-016-9453-4]
Factorization of Hermite subdivision operators preserving exponentials and polynomials
CONTI, COSTANZA;
2016
Abstract
In this paper we focus on Hermite subdivision operators that act on vector valued data interpreting their components as function values and associated consecu- tive derivatives. We are mainly interested in studying the exponential and polynomial preservation capability of such kind of operators, which can be expressed in terms of a generalization of the spectral condition property in the spaces generated by polynomials and exponential functions. The main tool for our investigation are con- volution operators that annihilate the aforementioned spaces, which apparently is a general concept in the study of various types of subdivision operators. Based on these annihilators, we characterize the spectral condition in terms of factorization of the subdivision operator.File | Dimensione | Formato | |
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