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Sectorial Extensions, via Laplace Transforms, in Ultraholomorphic Classes Defined by Weight Functions

Abstract: We prove several extension theorems for Roumieu ultraholomorphic classes of functions in sectors of the Riemann surface of the logarithm which are defined by means of a weight function or weight matrix. Our main aim is to transfer the results of V. Thilliez from the weight sequence case to these different, or more general, frameworks. The technique rests on the construction of suitable kernels for a truncated Laplace-like integral transform, which provides the solution without resorting to Whitney-type extension results for ultradifferentiable classes. As a byproduct, we obtain an extension in a mixed weight-sequence setting in which assumptions on the sequence are minimal.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Results in Mathematics, volume 74, Article number: 27 (2019)

Editorial: Springer

 Fecha de publicación: 14/01/2019

Nº de páginas: 44

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00025-018-0951-1

ISSN: 1422-6383,1420-9012

Proyecto español: MTM2016-77642-C2-1-P

Url de la publicación: https://doi.org/10.1007/s00025-018-0951-1