On extended Chebyshev systems with positive accuracy

Douglas D. Novaes, Joan Torregrosa

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. A classical necessary condition for an ordered set of n+1 functions F to be an ECT-system in a closed interval is that all the Wronskians do not vanish. With this condition all the elements of Span(F) have at most n zeros taking into account the multiplicity. Here the problem of bounding the number of zeros of Span(F) is considered as well as the effectiveness of the upper bound when some Wronskians vanish. For this case we also study the possible configurations of zeros that can be realized by elements of Span(F). An application to count the number of isolated periodic orbits for a family of nonsmooth systems is performed.
Original languageEnglish
Pages (from-to)171-186
JournalJournal of Mathematical Analysis and Applications
Volume448
Issue number1
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • ECT-system
  • Number of zeros of real functions
  • Zeros of Melnikov functions for nonsmooth systems

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