×

Approximation of entire harmonic functions in \(R^ 3\) having index-pair \((p,q)\). (English) Zbl 0756.41024

Summary: The authors define approximation error for harmonic functions in \(H_ R\), \(0<R<\infty\), the class of all harmonic functions \(H\) in \(R^ 3\), that are regular in the open ball \(D_ R\) of radius \(R\) centered at the origin and are continuous on the closure \(\overline D_ R\) of \(D_ R\); norm being the sup. norm. Necessary and sufficient conditions, in terms of the rate of decay of the approximation error \(E_ n(H,R)\), such that \(H\in H_ R\) has analytic continuation as an entire harmonic function having \((p,q)\)-order \(\rho\) and lower \((p,q)\)-order \(\lambda\), are obtained.

MSC:

41A25 Rate of convergence, degree of approximation
40C10 Integral methods for summability
41A30 Approximation by other special function classes
30E05 Moment problems and interpolation problems in the complex plane
PDFBibTeX XMLCite