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Bounds for the terms in a harmonic polynomial expansion
Published online by Cambridge University Press: 01 March 1998
Abstract
Let u be harmonic on the unit ball B of the Euclidean space ℝn, where n[ges ]2. There exist homogeneous harmonic polynomials uj of degree j such that [sum ]∞j=0uj converges absolutely and locally uniformly to u on B. We refer to the series [sum ]∞j=0uj, which is unique, as the polynomial expansion of u. By h∞ we denote the Hardy class of all bounded harmonic functions on B, and if u∈h∞, we write ∥u∥∞=supB[mid ]u[mid ].
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 2 , March 1998 , pp. 325 - 327
- Copyright
- Cambridge Philosophical Society 1998
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