On the Chebyshev property for a new family of functions

Armengol Gasull; J. Tomás Lázaro; Joan Torregrosa

doi:https://doi.org/10.1016/j.jmaa.2011.09.019

On the Chebyshev property for a new family of functions

Armengol Gasull, J. Tomás Lázaro, Joan Torregrosa

Department of Mathematics

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

14 Citations (Scopus)

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. © 2011 Elsevier Inc.

Original language	English
Pages (from-to)	631-644
Journal	Journal of Mathematical Analysis and Applications
Volume	387
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.09.019
Publication status	Published - 15 Mar 2012

Keywords

Chebyshev system
Derivation-Division algorithm
Limit cycles of planar systems
Number of zeroes of real functions

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https://ddd.uab.cat/record/150537

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AU - Gasull, Armengol

AU - Lázaro, J. Tomás

AU - Torregrosa, Joan

PY - 2012/3/15

Y1 - 2012/3/15

N2 - 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. © 2011 Elsevier Inc.

AB - 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. © 2011 Elsevier Inc.

KW - Chebyshev system

KW - Derivation-Division algorithm

KW - Limit cycles of planar systems

KW - Number of zeroes of real functions

U2 - https://doi.org/10.1016/j.jmaa.2011.09.019

DO - https://doi.org/10.1016/j.jmaa.2011.09.019

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EP - 644

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

On the Chebyshev property for a new family of functions

Abstract

Keywords

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