Conferencias plenarias

Congreso: Workshop on functional analysis and operator theory.


Lugar: UPV, Valencia, España.


Fechas: del 18 al 23 de septiembre de 2017.


Miembros del equipo conferenciantes:

Ponente y título: Javier Jiménez-Garrido, Growth indices for weight sequences and weight functions

Resumen:  When defining ultradifferentiable (or ultraholomorphic) classes of functions by means of weight sequences or functions, it is standard to impose some conditions on the weights in order to guarantee stability  (product,  derivation and composition closedness) and quasianaliticity properties. It turns out that many of them are related to, or can be expressed in terms of, the indices of O-Regular Variation studied by several authors (S. Aljan\v ci\'c, D. Arandelovi\'c, N.H. Bingham W.~Matuszewska, E. Seneta). In this talk, we will present this connection and we will also show the link between the indices for a weight sequence and the ones for its associated weight function. Finally, classical and new theorems  regarding the injectivity and surjectivity of the asymptotic Borel map will be stated in a simple way using these indices. Joint work with Javier Sanz (Universidad de Valladolid, Spain) and Gerhard Schindl (University of Vienna, Austria).

Ponente y título: Javier Sanz, Surjectivity of the Borel map in Roumieu ultraholomorphic classes in sectors

Resumen: WEB

Página web del congreso:

Congreso: Workshop on Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential,…) Equations 2017.

Lugar: UAH, Alcalá de Henares, España.

Fechas: del 4 al 8 de septiembre de 2017.

Miembros del equipo conferenciantes:

Ponente y título: Sergio A. Carrillo, Toward monomial multisummability.
Resumen: The goal of this talk is to introduce and develop a proposal to mix di erent levels of summability w.r.t.  monomials, a notion introduced in [1] to understand formal solutions of singularly perturbed di erential equations.  Following the ap- proach  of  Ecalle's  accelerator  operators  in  the  well-known  case  of  one  variable we  de ne  monomial  multisummability  for  series  in  several  variables  using  the characterization of this notion through Borel-Laplace like integral operators ob- tained in [2].  The need of this notions emerges naturally since there are series solutions of singularly perturbed di erential equations that are sums of monomi- ally summable series of di erent levels and thus can not be summed with simple monomial summability [3].
[1] Canalis-Durand M., Mozo-Fernandez J., Schafke R.:  Monomial summability and doubly singular di erential equations. J. Di erential Equations, vol. 233, (2007) 485511.
[2] Carrillo,  S.  A.,  Mozo-Fernandez,  J.  An  extension  of  Borel-Laplace  meth- ods  and  monomial  summability.  Submitted  to  publication.  Available  at
[3] Carrillo,  S.  A.,  Mozo-Fernandez,  J.  Tauberian  properties  for  monomial summability  with  appliactions  to  P a an  systems.  Journal  of  Di erential Equations 261 (2016) 7237-7255

Ponente y título: Javier Jiménez-Garrido, Multisummability in ultraholomorphic classes associated with log-convex sequences.

Resumen:  Summability of formal power series in a direction may be dealt with in the framework of ultraholomorphic classes associated with well behaved logarithmically convex sequences. After commenting on some fundamental aspects of this tool, we will put forward a concept of multisummability in a direction with respect to a nite, ordered family of sequences with different values of their growth index $\ommega(M)$ The acceleration kernels and operators in this context are constructed through a new concept of summability kernel. In order to handle the case where the equality of growth indices occur, we need to introduce a comparability notion between the sequences, and we will discuss which results remain true in this situation and which are the obstacles appearing. Joint work with Alberto Lastra (Universidad de Alcala, Spain), Shingo Kamimoto (Hiroshima University, Japan) and Javier Sanz (Universidad de Valladolid, Spain).


Ponente y título:  Alberto Lastra, On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference-differential initial value Cauchy problem.

Resumen: PDF.


Página web del congreso:


Workshop: Asymptotic and computational aspects of complex differential equations,
Centro di Ricerca Matematica Ennio De Giorgi. Pisa, Italia. 13 a 17 de Febrero, 2017.
Autor: Javier Sanz Gil
Título: Injectivity and surjectivity of the asymptotic Borel map in classes with log-convex constraints
Resumen: We will comment on classical and recent results on the injectivity and surjectivity of the Borel map in Carleman-Roumieu ultraholomorphic classes in sectors of the Riemann surface of the logarithm (in other words, classes of holomorphic functions admitting an asymptotic expansion at the vertex of the sector), with constraints given by a logarithmically convex sequence of positive real numbers. In many of these statements the opening of the region, and one of two suitable growth indices for log-convex sequences, will play a role. We will highlight some situations where these two indices agree, respectively are distinct.