On extended Chebyshev systems with positive accuracy

Douglas D. Novaes; Joan Torregrosa

doi:https://doi.org/10.1016/j.jmaa.2016.10.076

On extended Chebyshev systems with positive accuracy

Douglas D. Novaes, Joan Torregrosa

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

31 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 language	English
Pages (from-to)	171-186
Journal	Journal of Mathematical Analysis and Applications
Volume	448
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.10.076
Publication status	Published - 1 Apr 2017

Keywords

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

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AB - © 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.

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KW - Number of zeros of real functions

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

On extended Chebyshev systems with positive accuracy

Abstract

Keywords

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