On generalized Gaussian quadratures for bandlimited exponentials

We review the methods in Beylkin and Monzón (2002) [4], and Xiao et al. (2001) [24], for constructing quadratures for bandlimited exponentials and introduce a new algorithm for the same purpose. As in Beylkin and Monzón (2002) [4], our approach also yields generalized Gaussian quadratures for exponentials integrated against a non-sign-definite weight function. In addition, we compute quadrature weights via ℓ2 and ℓ∞ minimization and compare the corresponding quadrature errors.