2015/03/22 by Danchenko, V. I., Semin, L. A.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1503.06476
Sharp quadrature formulas for integrals of complex rational functions on circles, real axis and its segments are obtained. We also find sharp quadrature formulas for calculation of L2-norms of rational functions on such sets. Basing on quadrature formulas for rational functions, in particular, for simple partial fractions and polynomials, we derive sharp inequalities for different metrics (Nikol'skii type inequalities).