Shift generated Haar spaces on unbounded, closed domains in the complex plane (Q1884425)

The authors study here \(N\)-dimensional and universal and analytic Haar space generation for some closed sets \(F\) of \(C\). The space \(C^0(F)\) of all complex valued continuous functions \(f\) on \(F\) with \(\lim _{x\in F, z\rightarrow \infty} f(z) = 0 \), is investigated. Universal Haar space generators have been characterized in many cases here. It is also pointed out that in \(C^0(F)\) a best approximation by finite dimensional space \(V\) is unique if and only if \( V\) is a Haar space [cf. \textit{A. Haar}, Math. Ann. 78, 294--311 (1917; JFM 46.0418.01); \textit{A. N. Kolmogorov}, Usp. Mat. Nauk 3, 216--221 (1948; Zbl 0030.02803)].