The problem of existence and uniqueness of a quadrature formula with maximal trignonometric degree of precision for 2π-periodic functions with fixed number of free nodes of fixed different multiplicities at each node is considered. Our approach is based on some properties of the topological degree of a mapping with respect to an open bounded set and a given point. The explicit expression for the quadrature formulae with maximal trignometric degree of precision in the 2-periodic case of multiplicities is obtained. An error analysis for the quadrature with maximal trigonometric degree of precision is given. Classification (1991): 41A55, 65D30
Mathematics Subject
We characterize certain function classes in terms of the remainder in o~ co q_ the quadrature formula S_~of(x)dx=(~r/cr)Y~ .... f(ulr/cr) R~[f]. In the process, we prove a generalization of the famous theorem of Paley and Wiener about entire functions of exponential type belonging to L 2 on the real line.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.