RT Journal Article
T1 Convergence of polynomial level sets.
A1 Ferrera Cuesta, Juan
AB In 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.
PB American Mathematical Society
SN 0002-9947
YR 1998
FD 1998
LK https://hdl.handle.net/20.500.14352/57247
UL https://hdl.handle.net/20.500.14352/57247
LA eng
NO M. Baronti and P. Papini, Convergence of sequences of sets. In Methods of functional analysis in approximation theory, ISNM 76, Birkhäuser, Basel, 1986, pp. 133–155. G. Beer, Convergence of continuous linear functionals and their level sets, Arch. Math. 52 (1989), 482–491. J. M. Borwein and J. Vanderwerff, Dual Kadec-Klee norms and the relationships between Wijsman, slice and Mosco convergence, Michigan Math. J. 41 (1994), 371–387. J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1984. C. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966. J. Llavona, Approximation of continously differentiable functions, North-Holland Math. Studies, vol. 130, North-Holland, Amsterdam, 1986. J. Mujica, Complex analysis in Banach spaces, North-Holland Math. Studies, vol. 120, North-Holland, Amsterdam, 1986.
DS Docta Complutense
RD 16 may 2024