Hilbert boundary value problems—a distributional approach

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Abstract
Hilbert boundary value problems for a half-space are considered for analytic representations of Schwartz distributions: given data g ∈D'(ℛ) and a coefficient x we seek functions F(z) analytic for Jmz≠0 whose limits exist in D'(ℛ) and satisfy F+—XF– = g on an open subset U of the real line R. U is the complement of a finite set which contains the singular support and the zeros of X·X and its reciprocal satisfy certain growth conditions near the boundary points of U. Solutions F(z) are shown to exist, and their general form is determined by obtaining a suitable factorisation of x.

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