Conventional normal mode analysis often falls short in predicting a variety of transient phenomena in a non-self-adjoint (non-Hermitian) system. Laplace transform is capable of capturing all possible behavior in general systems. However, degenerate essential spectra require careful analysis. The Alfvén wave in a flowing plasma is an example in which the coalescence of the Alfvén singularities yields nonexponential growth of fluctuations. Invoking hyperfunction theory, rigorous expression of the Laplace transform leads to an accurate estimate of the asymptotic behavior of resonant singular modes.