ultrapolynomial

English

Etymology

ultra- +‎ polynomial

Noun

ultrapolynomial (plural ultrapolynomials)

1. (mathematics, rare) A power series in several variables $P:K^{d}\rightarrow K$ (with $K$ a field) of the form $P(x)=\Sigma _{\alpha \in \mathbb {N} ^{d}}c_{\alpha }x^{\alpha }$ 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 $P(z)$ of class $\left(M_{p}\right)$ (resp. of class $\left\{M_{p}\right\}$) such that $P$ does not vanish on $\mathbb {R} ^{d}$ and satisfies the following estimate:

Adjective

ultrapolynomial (not comparable)

1. Relating to ultrapolynomials.

Derived terms

• ultrapolynomially