On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities

We consider a Cauchy problem for some family of linear q-difference-differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables X (t, z) for given formal power series initial conditions. Under suitable conditions and by the appl...

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Detalles Bibliográficos
Autores: Lastra Sedano, Alberto|||0000-0002-4012-6471, Sanz, Javier, Malek, Stephane
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/41470
Acceso en línea:http://hdl.handle.net/10017/41470
https://dx.doi.org/10.1016/j.jde.2012.01.038
Access Level:acceso abierto
Palabra clave:q-Difference-differential equations
q-Laplace transform
Formal power series solutions
q-Gevrey asymptotic expansions
Small divisors
Fuchsian and irregular singularities
Matemáticas
Mathematics
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spelling On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularitiesLastra Sedano, Alberto|||0000-0002-4012-6471Sanz, JavierMalek, Stephaneq-Difference-differential equationsq-Laplace transformFormal power series solutionsq-Gevrey asymptotic expansionsSmall divisorsFuchsian and irregular singularitiesMatemáticasMathematicsWe consider a Cauchy problem for some family of linear q-difference-differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables X (t, z) for given formal power series initial conditions. Under suitable conditions and by the application of certain q-Borel and Laplace transforms (introduced by J.-P. Ramis and C. Zhang), we are able to deal with the small divisors phenomenon caused by the Fuchsian singularity, and to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion in t, uniformly for z in the compact sets of , is X (t, z) . The small divisorsʼ effect is an increase in the order of q-exponential growth and the appearance of a power of the factorial in the corresponding q-Gevrey bounds in the asymptotics.Elsevier20122012-05-15journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/41470https://dx.doi.org/10.1016/j.jde.2012.01.038reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/414702026-06-18T11:13:07Z
dc.title.none.fl_str_mv On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
title On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
spellingShingle On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
Lastra Sedano, Alberto|||0000-0002-4012-6471
q-Difference-differential equations
q-Laplace transform
Formal power series solutions
q-Gevrey asymptotic expansions
Small divisors
Fuchsian and irregular singularities
Matemáticas
Mathematics
title_short On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
title_full On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
title_fullStr On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
title_full_unstemmed On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
title_sort On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
dc.creator.none.fl_str_mv Lastra Sedano, Alberto|||0000-0002-4012-6471
Sanz, Javier
Malek, Stephane
author Lastra Sedano, Alberto|||0000-0002-4012-6471
author_facet Lastra Sedano, Alberto|||0000-0002-4012-6471
Sanz, Javier
Malek, Stephane
author_role author
author2 Sanz, Javier
Malek, Stephane
author2_role author
author
dc.subject.none.fl_str_mv q-Difference-differential equations
q-Laplace transform
Formal power series solutions
q-Gevrey asymptotic expansions
Small divisors
Fuchsian and irregular singularities
Matemáticas
Mathematics
topic q-Difference-differential equations
q-Laplace transform
Formal power series solutions
q-Gevrey asymptotic expansions
Small divisors
Fuchsian and irregular singularities
Matemáticas
Mathematics
description We consider a Cauchy problem for some family of linear q-difference-differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables X (t, z) for given formal power series initial conditions. Under suitable conditions and by the application of certain q-Borel and Laplace transforms (introduced by J.-P. Ramis and C. Zhang), we are able to deal with the small divisors phenomenon caused by the Fuchsian singularity, and to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion in t, uniformly for z in the compact sets of , is X (t, z) . The small divisorsʼ effect is an increase in the order of q-exponential growth and the appearance of a power of the factorial in the corresponding q-Gevrey bounds in the asymptotics.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-05-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/41470
https://dx.doi.org/10.1016/j.jde.2012.01.038
url http://hdl.handle.net/10017/41470
https://dx.doi.org/10.1016/j.jde.2012.01.038
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
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