RT Journal Article
T1 Smooth approximation of Lipschitz functions on Finsler manifolds
A1 Garrido, M. Isabel
A1 Jaramillo Aguado, Jesús Ángel
A1 Rangel, Yenny C.
AB We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f : M -> R defined on a connected, second countable Finsler manifold M, for each positive continuous function epsilon : M -> (0, infinity) and each r > 0, there exists a C-1-smooth Lipschitz function g : M -> R such that vertical bar f(x) - g(x)vertical bar <= epsilon(x), for every x is an element of M, and Lip(g) <= Lip(f) + r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebra C-b(1)(M) of all C-1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T : C-b(1)(N) -> C-b(1)(M) as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.
PB Hindawi
SN 0972-6802
YR 2013
FD 2013
LK https://hdl.handle.net/20.500.14352/33358
UL https://hdl.handle.net/20.500.14352/33358
LA eng
NO D.G.I. (Spain) Grant
NO (CDCHT-UCLA) (Venezuela)
DS Docta Complutense
RD 16 may 2024