2007/02/17 by Rufty, Alan
#31Bxx #35J99 #65D05 #86A22 #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.math-ph/0702064
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half ℝn plane, where fundamental solutions satisfy Laplace's equation, and the upper-half complex plane, where simple poles are of interest. This approach can handle higher-order pole fits, as well as logarithmic source fits, in the complex setting and it can handle higher-order multipole fits in the general real ℝn setting. Higher-order multipoles in the real ℝn half-space setting are of particular interest since fits based on a commonly used type of radial-basis function (inverse multiquadrics) can be reinterpreted as multipole based interpolations that minimize energy forms.