On extended chebyshev systems with positive accuracy
Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2017
Abstract:	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.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Ministerio de Ciencia e Innovación MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P European Commission 316338 European Commission 318999
Note:	Agraïments: The first author is supported by a FAPESP-BRAZIL grant 2013/16492-0. The second author is supported by UNAB13-4E-1604 grant.
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Document:	Article
Subject:	Number of zeros of real functions ; ECT-System ; Zeros of Melnikov ; Functions for non-smooth systems
Published in:	Journal of mathematical analysis and applications, Vol. 448 Núm. 1 (April 2017), p. 171-186, ISSN 1096-0813

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