Fourier quasi-integral expansions of functions and their applications to the solution of boundary value problems (Q2388044)

An integral representation is obtained for functions \(f\in C^{n+1}(\mathbb{R})\) such that \(f^{(n+1)}\in L^1(\mathbb{R})\) and \(f^{(n)}\) is a Fourier integral. This applies to a Dirchlet problem in a half-plane and to a generalized transmission problem in an unbounded three-layer medium.