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

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DOI: 10.4236/apm.2013.32033    5,213 Downloads   8,611 Views  
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. Cao, "Hilbert Boundary Value Problem with an Unknown Function on Arbitrary Infinite Straight Line," Advances in Pure Mathematics, Vol. 3 No. 2, 2013, pp. 235-239. doi: 10.4236/apm.2013.32033.

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