On the Distribution of Zeros and Poles of Rational Approximants on Intervals
| Autor: | V. V. Andrievskii, H.-P. Blatt, R. K. Kovacheva |
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| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Abstract and Applied Analysis, Vol 2012 (2012) |
| Druh dokumentu: | article |
| ISSN: | 1085-3375 1687-0409 |
| DOI: | 10.1155/2012/961209 |
| Popis: | The distribution of zeros and poles of best rational approximants is well understood for the functions 𝑓(𝑥)=|𝑥|𝛼, 𝛼>0. If 𝑓∈𝐶[−1,1] is not holomorphic on [−1,1], the distribution of the zeros of best rational approximants is governed by the equilibrium measure of [−1,1] under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, 𝑎-values, and poles of best real rational approximants of degree at most 𝑛 to a function 𝑓∈𝐶[−1,1] that is real-valued, but not holomorphic on [−1,1]. Generalizations to the lower half of the Walsh table are indicated. |
| Databáze: | Directory of Open Access Journals |
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