Address: Department of Mathematics, University of Vigo, Spain
E-mail: laia.francina.tugores@uvigo.gal
Abstract: This note deals with interpolation of values of analytic functions belonging to a given space, on finite sets of consecutive points of sequences in the disc, performed by rational functions and polynomials. Our goal is to identify sequences and spaces whose functions provide a bound of the error at the first uninterpolated point that is as small as desired. For certain sequences, we prove that this happens for bounded functions, Lipschitz functions and those that have derivatives in the disc algebra.
AMSclassification: primary 30E05; secondary 41A05.
Keywords: interpolation on sequences, bounded analytic function, Lipschitz class, disc algebra.
DOI: 10.5817/AM2025-2-85