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Some remarks on formal power series and formal Laurent series

In: Mathematica Slovaca, vol. 67, no. 3
Dariusz Bugajewski - Xiao-Xiong Gan
Detaily:
Rok, strany: 2017, 631 - 644
Kľúčové slová:
convolution, dot product, formal Laurent series, formal power series, non-Archimedean valuation, nonexpansive mapping, order, product (multiplication), spherical completeness, ultrametric
O článku:
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.:\textit{On formal Laurent series}, Bull. Braz. Math. Soc. \textbf{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.
Ako citovať:
ISO 690:
Bugajewski, D., Gan, X. 2017. Some remarks on formal power series and formal Laurent series. In Mathematica Slovaca, vol. 67, no.3, pp. 631-644. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0297

APA:
Bugajewski, D., Gan, X. (2017). Some remarks on formal power series and formal Laurent series. Mathematica Slovaca, 67(3), 631-644. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0297
O vydaní:
Publikované: 27. 6. 2017