Resumen de Polynomial approximation of polyharmonic functions on a complement of a John domain

Vladimir V. Andrievskii

• We prove a Jackson�Mergelyan type theorem on the uniform polynomial approximation of continuous polyharmonic functions on a set �without cusps on the boundary that point inside of the set�. We apply this theorem to derive a harmonic counterpart of a result by Mezhevich and Shirokov on the analytic polynomial approximation of continuous functions on a set consisting of two parallel segments.