Generalized Schwarzian derivatives and higher order differential equations

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dc.contributor.authorChuaqui, Martin
dc.contributor.authorGrohn, Janne
dc.contributor.authorRattya, Jouni
dc.date.accessioned2024-01-10T12:39:12Z
dc.date.available2024-01-10T12:39:12Z
dc.date.issued2011
dc.description.abstractIt is shown that the well-known connection between the second order linear differential equation h '' B(z) h = 0, with a solution base {h(1), h(2)}, and the Schwarzian derivative
dc.description.abstracts(f) = (f ''/f')' - 1/2(f ''/f')(2)
dc.description.abstractof f = h(1)/h(2), can be extended to the equation h((k)) + B(z) h = 0 where k >= 2. This generalization depends upon an appropriate definition of the generalized Schwarzian derivative S-k (f) of a function f which is induced by k - 1 ratios of linearly independent solutions of h((k)) + B(z) h = 0. The class R-k(Omega) of meromorphic functions f such that S-k(f) is analytic in a given domain Omega is also completely described. It is shown that if Omega is the unit disc D or the complex plane C, then the order of growth of f is an element of R-k(Omega) is precisely determined by the growth of S-k(f), and vice versa. Also the oscillation of solutions of h((k)) + B(z) h = 0, with the analytic coefficient B in D or C, in terms of the exponent of convergence of solutions is briefly discussed.
dc.description.funderAcademy of Finland
dc.description.funderFinnish Cultural Foundation
dc.description.funderVaisala Fund of Finnish Science and Letters
dc.description.funderMICINN, Spain
dc.description.funderJunta de Andalucia, Spain
dc.description.funderEuropean Science Foundation RNP HCAA
dc.description.funderFondecyt Grant
dc.description.funderMecesup Grant
dc.fechaingreso.objetodigital2024-04-25
dc.format.extent16 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1017/S0305004111000296
dc.identifier.eissn1469-8064
dc.identifier.issn0305-0041
dc.identifier.urihttps://doi.org/10.1017/S0305004111000296
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/77160
dc.identifier.wosidWOS:000294150900011
dc.information.autorucMatemática;Chuaqui M ;S/I;75421
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final354
dc.pagina.inicio339
dc.publisherCAMBRIDGE UNIV PRESS
dc.revistaMATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
dc.rightsacceso restringido
dc.subjectUNIVALENT-FUNCTIONS
dc.subjectUNIT DISC
dc.subjectSPACES
dc.subjectCOEFFICIENTS
dc.subjectGROWTH
dc.subject.ods08 Decent Work and Economic Growth
dc.subject.odspa08 Trabajo decente y crecimiento económico
dc.titleGeneralized Schwarzian derivatives and higher order differential equations
dc.typeartículo
dc.volumen151
sipa.codpersvinculados75421
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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