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arXiv · 2602.21056

Oppenheim--Schur inequalities for causal products

Dominique Guillot·Javad Mashreghi·Prateek Kumar Vishwakarma
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Abstract

We establish a class of Oppenheim--Schur-type inequalities for the convolutional Jury product of positive semidefinite matrices. These results extend to a causal convolutional setting the classical Schur and Oppenheim inequalities associated with the Hadamard product. Our approach highlights structural parallels between entrywise and convolution-based matrix operations, revealing how positivity constraints interact with causality. Building on this perspective, we introduce a broader family of causal matrix products and prove unified inequalities that simultaneously recover the classical Schur and Oppenheim bounds as well as their convolutional Jury counterparts. These results provide a common framework for understanding positivity-preserving matrix products and suggest further connections between classical matrix analysis and causal operator structures.

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BibTeXRIS

Dominique Guillot, Javad Mashreghi, Prateek Kumar Vishwakarma. 2026-02-24. Oppenheim--Schur inequalities for causal products. https://arxiv.org/abs/2602.21056

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