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

被引：0
作者：
Javier Jiménez-Garrido
Javier Sanz
Gerhard Schindl
机构：
[1] Universidad de Valladolid,Departamento de Álgebra, Análisis Matemático, Geometría y Topología, Facultad de Ciencias
[2] Universidad de Valladolid,Instituto de Investigación en Matemáticas IMUVA
来源：
Results in Mathematics | 2019年 / 74卷
关键词：
Ultraholomorphic classes; weight sequences; functions and matrices; Legendre conjugates; Laplace transform; extension operators; indices of O-regular variation; 46E10; 30E05; 26A12; 44A05;
D O I：
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摘要：
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.
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