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
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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.
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.
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