C1-equivalence of functions near isolated degenerate critical points in Banach space

George K. Francis

Research output: Contribution to journalArticle

Abstract

We prove two theorems of N. Kuiper by standard methods of the calculus on Banach spaces. C0-sufficiency for Cr-functions of the r-jet of a real valued Cr-function of lowest degree r0 ≥ 2 on a Hilbert space follows from Kuiper's condition Q(r) also on a Banach space endowed with smooth partitions of unity. A new proof is given of the C1-sufficiency for Cr + p-functions, p ≥ r - r0, of the r + p-jet of a Q(r)-function on Hilbert space that also holds on Banach space modulo a further condition on the behavior of the function near its degenerate critical point.

Original languageEnglish (US)
Pages (from-to)331-337
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume32
Issue number2
DOIs
StatePublished - Nov 1970

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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