A LIPSCHITZ FUNCTION WHICH IS C-infinity ON AE LINE NEED NOT BE GENERICALLY DIFFERENTIABLE

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10189660" target="_blank" >RIV/00216208:11320/13:10189660 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/cm131-1-3" target="_blank" >http://dx.doi.org/10.4064/cm131-1-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/cm131-1-3" target="_blank" >10.4064/cm131-1-3</a>

Result language
angličtina
Original language name
A LIPSCHITZ FUNCTION WHICH IS C-infinity ON AE LINE NEED NOT BE GENERICALLY DIFFERENTIABLE
Original language description
We construct a Lipschitz function f on X = R-2 such that, for each 0 not equal nu is an element of X, the function f is C-infinity smooth on a.e. line parallel to v and f is Gateaux non-differentiable at all points of X except a first category set. Consequently, the same holds if X (with dim X > 1) is an arbitrary Banach space and "a.e." has any usual "measure sense". This example gives an answer to a natural question concerning the author's recent study of linearly essentially smooth functions (which generalize essentially smooth functions of Borwein and Moors).
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP201%2F12%2F0436" target="_blank" >GAP201/12/0436: Theory of Real Functions and Descriptive Set Theory III</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)