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Hilbert Boundary Value Problem with an Unknown Function on Arbitrary Infinite Straight Line
Mathematics College, Northeast Petroleum University, Daqing, China
- 1 Mathematics College, Northeast Petroleum University, Daqing, China
Advances in Pure Mathematics·Volume 03 (2013)·Pages 235–239·Published 5 March 2013·DOI10.4236/apm.2013.32033
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Abstract
We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann boundary value problem, and address it by defining symmetric extension for holomorphic functions about an arbitrary straight line passing through the origin. Finally, we develop the general solution and the solvable conditions for the Hilbert boundary value problem.
KeywordsArbitrary Infinite Straight LineSymmetric ExtensionHilbert Boundary Value ProblemUnknown
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