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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10189660%21RIV14-GA0-11320___
rdf:type
n11:Vysledek skos:Concept
rdfs:seeAlso
http://dx.doi.org/10.4064/cm131-1-3
dcterms: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 %22a.e.%22 has any usual %22measure sense%22. 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). 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 %22a.e.%22 has any usual %22measure sense%22. 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).
dcterms:title
A LIPSCHITZ FUNCTION WHICH IS C-infinity ON AE LINE NEED NOT BE GENERICALLY DIFFERENTIABLE A LIPSCHITZ FUNCTION WHICH IS C-infinity ON AE LINE NEED NOT BE GENERICALLY DIFFERENTIABLE
skos:prefLabel
A LIPSCHITZ FUNCTION WHICH IS C-infinity ON AE LINE NEED NOT BE GENERICALLY DIFFERENTIABLE A LIPSCHITZ FUNCTION WHICH IS C-infinity ON AE LINE NEED NOT BE GENERICALLY DIFFERENTIABLE
skos:notation
RIV/00216208:11320/13:10189660!RIV14-GA0-11320___
n11:predkladatel
n12:orjk%3A11320
n4:aktivita
n17:P
n4:aktivity
P(GAP201/12/0436)
n4:cisloPeriodika
1
n4:dodaniDat
n6:2014
n4:domaciTvurceVysledku
n15:7357362
n4:druhVysledku
n19:J
n4:duvernostUdaju
n9:S
n4:entitaPredkladatele
n13:predkladatel
n4:idSjednocenehoVysledku
58690
n4:idVysledku
RIV/00216208:11320/13:10189660
n4:jazykVysledku
n5:eng
n4:klicovaSlova
functions C-infinity on a.e. line.; Lipschitz function; essentially smooth functions; Gateaux differentiability
n4:klicoveSlovo
n7:Lipschitz%20function n7:functions%20C-infinity%20on%20a.e.%20line. n7:essentially%20smooth%20functions n7:Gateaux%20differentiability
n4:kodStatuVydavatele
PL - Polská republika
n4:kontrolniKodProRIV
[256F2BC0FCDC]
n4:nazevZdroje
Colloquium Mathematicum
n4:obor
n16:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:projekt
n14:GAP201%2F12%2F0436
n4:rokUplatneniVysledku
n6:2013
n4:svazekPeriodika
131
n4:tvurceVysledku
Zajíček, Luděk
n4:wos
000324842500003
s:issn
0010-1354
s:numberOfPages
11
n8:doi
10.4064/cm131-1-3
n10:organizacniJednotka
11320