扇形区域中卡尔曼 - 鲁米厄超全纯类中的最优平坦函数
Optimal Flat Functions in Carleman-Roumieu Ultraholomorphic Classes in Sectors.
作者信息
Jiménez-Garrido Javier, Miguel-Cantero Ignacio, Sanz Javier, Schindl Gerhard
机构信息
Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. de los Castros, s/n, 39005 Santander, Spain.
Instituto de Investigación en Matemáticas IMUVA, Universidad de Valladolid, Valladolid, Spain.
出版信息
Results Math. 2023;78(3):98. doi: 10.1007/s00025-023-01859-w. Epub 2023 Mar 14.
We construct optimal flat functions in Carleman-Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn'kin. Finally, we discuss some examples (including the well-known -Gevrey case) where such optimal flat functions can be obtained in a more explicit way.
我们在与一般强非拟解析权序列相关联的卡尔曼 - 鲁米厄超全纯类中构造最优平坦函数，这些函数定义在开口适当受限的扇形区域上。针对 Dyn'kin 意义下正则权序列的情况，给出了一个通用程序，以获得线性连续延拓算子，即博雷尔映射的右逆。最后，我们讨论一些例子（包括著名的 - 热夫雷情形），在这些例子中可以更明确地得到此类最优平坦函数。
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