Harmonicity Modulus and Applications to the Approximation by Polyharmonic Functions
arXiv:1005.49704 citationsh-index: 12
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AI Analysis
Provides a theoretical framework for approximation by polyharmonic functions, extending classical polynomial approximation results to a new function class.
The paper introduces the harmonicity modulus and harmonicity K-functional, and uses them to prove a Jackson-type theorem for approximating continuous functions by polyharmonic functions.
In the present paper we introduce the notion of harmonicity modulus and harmonicity K-functional and apply these notions to prove a Jackson type theorem for approximation of continuous functions by polyharmonic functions. For corresponding results on approximation by polynomials see [3, 7].