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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Quadrature and harmonic $ L\sp 1$-approximation in annuli


Authors: D. H. Armitage and M. Goldstein
Journal: Trans. Amer. Math. Soc. 312 (1989), 141-154
MSC: Primary 31B05; Secondary 41A30
DOI: https://doi.org/10.1090/S0002-9947-1989-0949896-5
MathSciNet review: 949896
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Abstract: Open sets $ D$ in $ {R^N}\;(N \geq 3)$ with the property that $ \bar D$ is a closed annulus $ \{ x:{r_1} \leq \;\left\Vert x\right\Vert \; \leq {r_2}\} $ are characterized by quadrature formulae involving mean values of certain harmonic functions. One such characterization is used to give a criterion for the existence of a best harmonic $ {L^1}$ approximant to a function which is subharmonic (and satisfies some other conditions) in an annulus.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0949896-5
Article copyright: © Copyright 1989 American Mathematical Society