Smooth Approximation of Lipschitz Functions on Finsler Manifolds
Joint Authors
Garrido, M. I.
Rangel, Y. C.
Jaramillo, J. A.
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-29
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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 ε:M→(0,∞) and each r>0, there exists a C1-smooth Lipschitz function g:M→ℝ such that |f(x)-g(x)|≤ε(x), for every x∈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 Cb1(M) of all C1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T:Cb1(N)→Cb1(M) as composition operators.
From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.
American Psychological Association (APA)
Garrido, M. I.& Jaramillo, J. A.& Rangel, Y. C.. 2013. Smooth Approximation of Lipschitz Functions on Finsler Manifolds. Journal of Function Spaces،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1006011
Modern Language Association (MLA)
Garrido, M. I.…[et al.]. Smooth Approximation of Lipschitz Functions on Finsler Manifolds. Journal of Function Spaces No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-1006011
American Medical Association (AMA)
Garrido, M. I.& Jaramillo, J. A.& Rangel, Y. C.. Smooth Approximation of Lipschitz Functions on Finsler Manifolds. Journal of Function Spaces. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1006011
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1006011