On solutions of linear equations with polynomial coefficients

被引：2

作者：

Adamus, Janusz ^{[1
]}

Seyedinejad, Hadi ^{[1
]}

机构：

[1] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada

来源：

ANNALES POLONICI MATHEMATICI | 2018年 / 121卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

arc-analytic function; Nash regulous function; semialgebraic geometry; ARC-ANALYTIC FUNCTIONS;

D O I：

10.4064/ap171122-29-12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a linear functional equation with polynomial coefficients need not admit an arc-analytic solution even if it admits a continuous semialgebraic one. We also show that such an equation need not admit a Nash regulous solution even if it admits an arc-analytic one.

引用

页码：1 / 6

页数：6

共 50 条

[31] Apparent singularities of linear difference equations with polynomial coefficients
S. A. Abramov
M. A. Barkatou
M. van Hoeij
Applicable Algebra in Engineering, Communication and Computing, 2006, 17 : 117 - 133
[32] Computation of the Asymptotics of Solutions for Equations with Polynomial Degeneration of the Coefficients
Kats, D. S.
DIFFERENTIAL EQUATIONS, 2015, 51 (12) : 1589 - 1594
[33] Small solutions to systems of polynomial equations with integer coefficients
Cipu, Mihai
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2011, 19 (02): : 89 - 99
[34] Computation of the asymptotics of solutions for equations with polynomial degeneration of the coefficients
D. S. Kats
Differential Equations, 2015, 51 : 1589 - 1594
[35] PROBLEM OF CONNECTION OF FUNDAMENTAL FAMILIES OF SOLUTIONS FOR A SYSTEM OF LINEAR-DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS
KOVALEVSKII, MA
SIBERIAN MATHEMATICAL JOURNAL, 1990, 31 (01) : 67 - 81
[36] Mean value theorems for polynomial solutions of linear elliptic equations with constant coefficients in the complex plane
Trofymenko O.D.
Journal of Mathematical Sciences, 2021, 254 (3) : 439 - 443
[37] Programs for constructing rational solutions to linear difference and q-difference equations with polynomial coefficients
Programmirovanie, (03): : 23 - 30
[38] Programs for constructing rational solutions to linear difference and q-difference equations with polynomial coefficients
Ryabenko, AA
PROGRAMMING AND COMPUTER SOFTWARE, 1997, 23 (03) : 136 - 141
[39] Chebyshev polynomial solutions of systems of high-order linear differential equations with variable coefficients
Akyüz, A
Sezer, M
APPLIED MATHEMATICS AND COMPUTATION, 2003, 144 (2-3) : 237 - 247
[40] POLYNOMIAL SOLUTIONS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
Petropoulou, Eugenia N.
Siafarikas, Panayiotis D.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (03) : 1053 - 1065

← 1 2 3 4 5 →