Monomial functions, normal polynomials and polynomial equations

被引:0
|
作者
Eszter Gselmann
Mehak Iqbal
机构
[1] University of Debrecen,Department of Analysis
[2] University of Debrecen,Doctoral School of Mathematical and Computational Sciences
来源
Aequationes mathematicae | 2023年 / 97卷
关键词
Generalized monomial; Quadratic function; Normal polynomial; Polynomial equation; Homomorphism; Derivation; Higher order derivation; Primary 39B55; Secondary 39B72;
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摘要
In this paper we consider generalized monomial functions f,g:F→C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f, g:{\mathbb {F}}\rightarrow {\mathbb {C}}$$\end{document} (of possibly different degree) that also fulfill f(P(x))=Q(g(x))x∈F,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} f(P(x))= Q(g(x)) \qquad \left( x\in {\mathbb {F}}\right) , \end{aligned}$$\end{document}where P∈F[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P\in {\mathbb {F}}[x]$$\end{document} and Q∈C[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q\in {\mathbb {C}}[x]$$\end{document} are given (classical) polynomials.
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页码:1059 / 1082
页数:23
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