On the approximation of real continuous functions by series of solutions of a single system of partial differential equations

• Autorzy: Carsten Elsner
• Języki publikacji: EN

Abstrakty

EN

We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function $f: ℝ^{s} → ℝ$ can be approximated with arbitrary accuracy by an infinite sum
$∑_{r=1}^{∞} H_{r}(x₁,...,x_{s}) ∈ C^{∞}(ℝ^{s})$
of analytic functions $H_{r}$, each solving the same system of universal partial differential equations, namely
$P(x_{σ};H_r,∂H_{r}/∂x_{σ},...,∂⁵H_{r}/∂x⁵_{σ}⁵) = 0$ (σ = 1,..., s).

Kategorie tematyczne

• 34A05: Explicit solutions and reductions
• 35C05: Solutions in closed form
• 26E10: C ∞ -functions, quasi-analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 104
• Numer: 1
• Strony: 57-84

Daty

wydano

2006

Twórcy

autor

Carsten Elsner

• Institut für Mathematik, Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

Identyfikatory

DOI

10.4064/cm104-1-4