具有 Gelfand-Shilov 与 Pilipović 核的算子的分解与奇异值估计
泛函分析
2016-04-05 v2
摘要
我们证明任何核属于 Pilipović 或 Gelfand-Shilov 空间的线性算子均可被同类中的两个算子分解。我们还给出了此类合成的数值逼近联系。我们应用这些合成规则推导奇异值估计，并为此类算子建立 Schatten-von Neumann 性质。
引用
@article{arxiv.1511.06257,
title = {Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovi\'c kernels},
author = {Yuanyuan Chen and Mikael Signahl and Joachim Toft},
journal= {arXiv preprint arXiv:1511.06257},
year = {2016}
}
备注
29 pages. We extend results in "Decompositions of Gelfand-Shilov (GS) kernels into kernels of similar class" arXiv:1112.4314 to include operator kernels in Pilipovic spaces. Note that the family of Pilipovic spaces contains the Fourier invariant GS-spaces. We also deduce suitable singular value estimate, and present certain characterizations of operators with kernels in Pilipovic spaces