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Hilbert Boundary Value Problem with an Unknown Function on Arbitrary Infinite Straight Line

Author(s): Lixia Cao

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 02;
Start page: 235;
Date: 2013;
Original page

Keywords: Arbitrary Infinite Straight Line | Symmetric Extension | Hilbert Boundary Value Problem | Unknown

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.
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