On the Chebyshev property for a new family of functions
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2012
Abstract:	We analyze whether a given set of analytic functions is an Extended Chebyshev system. This family of functions appears studying the number of limit cycles bifurcating from some nonlinear vector field in the plane. Our approach is mainly based on the so called Derivation-Division algorithm. We prove that under some natural hypotheses our family is an Extended Chebyshev system and when some of them are not fulfilled then the set of functions is not necessarily an Extended Chebyshev system. One of these examples constitutes an Extended Chebyshev system with high accuracy.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Ministerio de Ciencia e Innovación MTM2009-06973 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Chebyshev system ; Number of zeroes of real functions ; Derivation-Division algoritm ; Limit cycles of planar systems
Published in:	Journal of mathematical analysis and applications, Vol. 387 (2012) , p. 631-644, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2011.09.019

Postprint 19 p, 406.0 KB

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