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On zeros and boundary behavior of bounded harmonic functions
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Samianathan Ponnusamy
Published/Copyright:
April 19, 2010
Abstract
We study the connection between multiplicities of the zeros and boundary behavior of bounded analytic and harmonic functions. We prove existence of angular (non-tangential) limit at a boundary point provided that multiplicities of zeroes of the function grow fast enough on a given sequence of points approaching the boundary.
Published Online: 2010-04-19
Published in Print: 2010-04
© by Oldenbourg Wissenschaftsverlag, München, Germany
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Keywords for this article
analytic and planar harmonic functions;
angular limits;
multiplicity of zeroes
Articles in the same Issue
- To the theory of anisotropic plane elasticity
- The oblique derivative problem for second order nonlinear equations of mixed type with two degenerate lines
- On the length of level sets of real functions
- Green´s functions on the Heisenberg group
- Mixed boundary value problems for higher-order complex partial differential equations
- Part I: Theory of potential of convergence Part II: Applications in the field of ordinary differential equations
- On zeros and boundary behavior of bounded harmonic functions
