2011•Journal of Sichuan Normal UniversityRequires access
Inverse Hilbert Boundary Value Problems in Half Plane
Minghua Wang
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Abstract
Inverse problems are boundary value problems with parametric unknown functions.They possess important mechanical backgrounds.The study on the inverse boundary value problems is on the primary stage.In this paper,the mathematical formulation of a class of inverse Hilbert boundary value problems in half plane for analytic functions is given.On the basis of the classical theory of Riemann boundary value problems for analytic functions on real axis,the solvability of the inverse Hilbert boundary value problems is discussed by transforming them into Riemann boundary value problems.The real freedom of the solutions determined by the index of the inverse Hilbert boundary value problems is obtained.The solvable conditions and the integral representation of the solutions of the inverse Hilbert boundary value problems are also obtained.