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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). (en)
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 (en)
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 (en)
skos:notation
  • RIV/00216208:11320/13:10189660!RIV14-GA0-11320___
http://linked.open...avai/riv/aktivita
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  • P(GAP201/12/0436)
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  • 1
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  • 58690
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  • RIV/00216208:11320/13:10189660
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  • functions C-infinity on a.e. line.; Lipschitz function; essentially smooth functions; Gateaux differentiability (en)
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  • PL - Polská republika
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  • [256F2BC0FCDC]
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  • Colloquium Mathematicum
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  • 131
http://linked.open...iv/tvurceVysledku
  • Zajíček, Luděk
http://linked.open...ain/vavai/riv/wos
  • 000324842500003
issn
  • 0010-1354
number of pages
http://bibframe.org/vocab/doi
  • 10.4064/cm131-1-3
http://localhost/t...ganizacniJednotka
  • 11320
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