On the approximation of real continuous functions by series of solutions of a single system of partial differential equations
Carsten Elsner
Colloquium Mathematicae, Tome 106 (2006), p. 57-84 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function f:ℝs→ℝ can be approximated with arbitrary accuracy by an infinite sum ∑r=1∞Hr(x₁,...,xs)∈C∞(ℝs) of analytic functions Hr, each solving the same system of universal partial differential equations, namely P(xσ;Hr,∂Hr/∂xσ,...,∂⁵Hr/∂x⁵σ⁵)=0 (σ = 1,..., s).

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:284024 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-1-4,
     author = {Carsten Elsner},
     title = {On the approximation of real continuous functions by series of solutions of a single system of partial differential equations},
     journal = {Colloquium Mathematicae},
     volume = {106},
     year = {2006},
     pages = {57-84},
     zbl = {1095.41018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-1-4}
}

Carsten Elsner. On the approximation of real continuous functions by series of solutions of a single system of partial differential equations. Colloquium Mathematicae, Tome 106 (2006) pp. 57-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-1-4/