Ferrera Cuesta, Juan2023-06-202023-06-2019980002-994710.1090/S0002-9947-98-02342-3https://hdl.handle.net/20.500.14352/57247In this paper we give a characterization of pointwise and uniform convergence of sequences of homogeneous polynomials on a Banach space by means of the convergence of their level sets. Results are obtained both in the real and the complex cases, as well as some generalizations to the nonhomogeneous case and to holomorphic functions in the complex case. Kuratowski convergence of closed sets is used in order to characterize pointwise convergence. We require uniform convergence of the distance function to get uniform convergence of the sequence of polynomials.engConvergence of polynomial level sets.journal articlehttp://www.ams.org/journals/tran/1998-350-12/S0002-9947-98-02342-3/S0002-9947-98-02342-3.pdfhttp://www.ams.org/restricted access517.986.6517.518.45Polynomials in Banach spacesSet convergenceLevel setsSequences of homogeneous polynomials on a Banach spaceAnálisis matemático1202 Análisis y Análisis Funcional