We consider systems of exponentials that are orthogonal to measures dσ of a special form on (-a, a). Under certain conditions on the summation method, these systems form summation bases in L~p(-a, a) and in C_0 (the subspace of C[-a, a] orthogonal to dσ). With respect to these systems, Lipschitzian functions in C_0 are expanded into non-harmonic Fourier series that converge uniformly on [-a, a].
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