In principle, one can use the convolution theorem to evaluate the expression in Eq. 41. As such, one just have to separately evaluate the Fourier transform of both κ and G, then multiply them together and inverse Fourier transform them to get the analytic answer of k VSC . Here, both κ(ω) and G(ω) are square-integrable functions, we can extend the integral to -∞ by analytical continuation of κ(ω) and G(ω), and replace ω 0 with a variable ω, resulting in On the other hand,