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Expansions with Poisson kernels and related topics
Published online by Cambridge University Press: 12 January 2010
Abstract
Let P(r, θ) be the two-dimensional Poisson kernel in the unit disc D. It is proved that there exists a special sequence {ak} of points of D which is non-tangentially dense for ∂D and such that any function on ∂D can be expanded in series of P(|ak|, (·)–arg ak) with coefficients depending continuously on f in various classes of functions. The result is used to solve a Cauchy-type problem for Δu = μ, where μ is a measure supported on {ak}.
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 153 - 173
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- Copyright © Edinburgh Mathematical Society 2010
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