arXiv Open Access 2024

Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces

Stefan Kindermann Bernd Hofmann

Lihat Sumber

Abstrak

We consider the composition of operators with non-closed range in Hilbert spaces and how the nature of ill-posedness is affected by their composition. Specifically, we study the \mbox{Hausdorff-,} Cesàro-, integration operator, and their adjoints, as well as some combinations of those. For the composition of the Hausdorff- and the Cesàro-operator, we give estimates of the decay of the corresponding singular values. As a curiosity, this provides also an example of two practically relevant non-compact operators, for which their composition is compact. Furthermore, we characterize those operators for which a composition with a non-compact operator gives a compact one.

Topik & Kata Kunci

math.FA

Penulis (2)

Stefan Kindermann

Bernd Hofmann

Format Sitasi

APA MLA BibTeX

Kindermann, S., Hofmann, B. (2024). Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces. https://arxiv.org/abs/2401.14701

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓