Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovi\'c kernels
Functional Analysis
2016-04-05 v2
Abstract
We prove that any linear operator with kernel in a Pilipovi\'c or Gelfand-Shilov space can be factorized by two operators in the same class. We also give links on numerical approximations for such compositions. We apply these composition rules to deduce estimates of singular values and establish Schatten-von Neumann properties for such operators.
Keywords
Cite
@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}
}
Comments
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