英和和英

名詞

ultrapolynomial (複数形 ultrapolynomials)

1. (mathematics, rare) A power series in several variables ${\displaystyle P:K^{d}\rightarrow K}$ (with ${\displaystyle K}$ a field) of the form ${\displaystyle P(x)=\Sigma _{\alpha \in \mathbb {N} ^{d}}c_{\alpha }x^{\alpha }}$ whose coefficients are bounded in some specific sense.
   • 2015, Stevan Pilipovic, Bojan Prangoski, Jasson Vindas, “On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution”, in arXiv‎^[1]:

     There exists an ultrapolynomial ${\displaystyle P(z)}$ of class ${\displaystyle \left(M_{p}\right)}$ (resp. of class ${\displaystyle \left\{M_{p}\right\}}$) such that ${\displaystyle P}$ does not vanish on ${\displaystyle \mathbb {R} ^{d}}$ and satisfies the following estimate: