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Integral representations for harmonic functions of infinite order in a cone. (English) Zbl 1252.31004
Summary: A harmonic function of infinite order defined in an n-dimensional cone and continuous in the closure can be represented in terms of the modified Poisson integral and an infinite sum of harmonic polynomials vanishing on the boundary.
MSC:
31B10Integral representations of harmonic functions (higher-dimensional)
31C05Generalizations of harmonic (subharmonic, superharmonic) functions
References:
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[10]Siegel D., Talvila E.: Sharp growth estimates for modified Poisson integrals in a half space. Potential Anal. 15, 333–360 (2001) · Zbl 0987.31003 · doi:10.1023/A:1011817130061
[11]Yoshida H., Miyamoto I.: Solutions of the Dirichlet problem on a cone with continuous data. J. Math. Soc. Jpn. 50(1), 71–93 (1998) · Zbl 0907.31001 · doi:10.2969/jmsj/05010071
[12]Yoshida H., Miyamoto I.: Harmonic functions in a cone which vanish on the boundary. Math. Nachr. 202, 177–187 (1999) · Zbl 0929.31001 · doi:10.1002/mana.19992020115