SOME REMARKS ON FORMAL POWER SERIES AND FORMAL LAURENT SERIES

被引：2

作者：

Bugajewski, Dariusz ^{[1
]}

Gan, Xiao-Xiong ^{[2
]}

机构：

[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, Umultowska 87, PL-6161 Poznan, Poland

[2] Morgan State Univ, Dept Math, Baltimore, MD 21251 USA

来源：

MATHEMATICA SLOVACA | 2017年 / 67卷 / 03期

关键词：

convolution; dot product; formal Laurent series; formal power series; non-Archimedean valuation; nonexpansive mapping; order; product (multiplication); spherical completeness; ultrametric; RIORDAN MATRICES;

D O I：

10.1515/ms-2016-0297

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we consider the topology on the set of formal Laurent series induced by the ultrametric defined via the order. In particular, we establish that the product of formal Laurent series, considered in [GAN, X. X.-BUGAJEWSKI, D.:On formal Laurent series, Bull. Braz. Math. Soc. 42 (2011), 415-437], is not continuous. We also show some applications of fixed point theorems to some nonlinear mappings defined on the space of formal power series or on the space of formal Laurent series. Finally, in the second part of the paper, we propose another approach to study of dot product and multiplication of formal Laurent series, in particular establishing integral representation of dot product and convolution representation of multiplication. (C) 2017 Mathematical Institute Slovak Academy of Sciences

引用

页码：631 / 644

页数：14

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