2008/09/30 by Werner Haußmann, Haussmann, Werner, Ognyan Kounchev +1
Computer Science · Engineering · Mathematics · #31B30 #41A05 #65D05 #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Numerical methods for differential equations #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.0809.5159
openalex publication_date 2008/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from C∞ or analytic functions in the ball BR. We prove two main results on the interpolation of C∞ or analytic functions f in the ball BR by polyharmonic functions h of a given order of polyharmonicity p.