On the computation of the Fourier transform under the presence of nearby polar singularities

摘要

In this paper we present a procedure for the computation ofintegrals on the whole real line with nearby singularities. Themethod is based in collecting the possible singularities of theintegrand within a weight function on the real line, passing to theunit circle by considering an associated weight function there andthen making use of Szego or interpolatory-type quadratureformulas. This algorithm is applied in order to provide acomputational method for the Fourier transform of a functionexhibiting polar singularities near the range of integration. Someerror bounds for the estimations are presented and some numericalexperiments carried out.