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A NEW METHOD FOR SOLVING THE HILBERT BOUNDARY VALUE PROBLEM FOR SEVERAL UNKNOWN FUNCTIONS,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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A new method is presented for solving a homogeneous Hilbert problem by reducing it to a new system of Fredholm integral equations which is obtainable in a way comparatively simpler than by the Plemelj system. The homogeneous Hilbert problem considered is given. The following theorem is proved if the connected problem does not have vanishing-in-the-infinity solutions, the obtained equation can be solved, and each solution of this equation yields a definite solution of the problem considered. A procedure is outlined for constructing a canonical system for solving the Hilbert problem. Author
APPROVED FOR PUBLIC RELEASE