Author:
Klintborg Markus,Olofsson Anders
Abstract
AbstractWe consider a class of generalized harmonic functions in the open unit disc in the complex plane. Our main results concern a canonical series expansion for such functions. Of particular interest is a certain individual generalized harmonic function which suitably normalized plays the role of an associated Poisson kernel.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis
Reference22 articles.
1. Ahern, P., Bruna, J., Cascante, C.: $$H^p$$-theory for generalized $${\cal{M}}$$-harmonic functions in the unit ball. Indiana Univ. Math. J. 45, 103–135 (1996)
2. Ahern, P., Cascante, C.: Exceptional sets for Poisson integrals of potentials on the unit sphere in $${\mathbb{C}^n}$$, $$p\le 1$$. Pac. J. Math. 153, 1–13 (1992)
3. Andrews, G.E., Askey, R., Roy, R.: Special Functions. Encyclopedia of Mathematics and its Applications, vol. 71. Cambridge University Press, Cambridge (1999)
4. Astala, K., Päivärinta, L.: Calderón’s inverse conductivity problem in the plane. Ann. Math. 163, 265–299 (2006)
5. Behm, G.: Solving Poisson’s equation for the standard weighted Laplacian in the unit disc (2014). arXiv:1306.2199v2 [math.AP]
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