Regularity and Compactness Properties of Integral Hankel Operators and Their Singular Vectors

Guiver, Chris

Abstract

Integral Hankel operators on vector-valued $L^2(\mathbb{R}_+,U)$-function spaces are considered. Regularity (integrability) and compactness properties of the kernel are shown to give rise to quantifiable regularity and compactness properties of the Hankel operator, and consequently of the associated singular vectors (also called Schmidt pairs), which finds relevance in model order reduction schemes. As demonstrated, strong- Lebesgue and Sobolev spaces naturally arise in the case that U is infinite dimensional. The theory is illustrated with examples.

Citation

Guiver, C. (2024). Regularity and Compactness Properties of Integral Hankel Operators and Their Singular Vectors. Complex Analysis and Operator Theory, 19, Article 6. https://doi.org/10.1007/s11785-024-01627-w

• Journal Article Type: Article
• Acceptance Date: Nov 11, 2024
• Online Publication Date: Nov 29, 2024
• Publication Date: 2024
• Deposit Date: Nov 25, 2024
• Publicly Available Date: Nov 29, 2024
• Print ISSN: 1661-8254
• Electronic ISSN: 1661-8262
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 19
• Article Number: 6
• DOI: https://doi.org/10.1007/s11785-024-01627-w
• Keywords: compact operator, integral Hankel operator, model order reduction, systems and control theory, singular vectors, Schmidt pairs