Oppenheim--Schur inequalities for causal products
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917291985207296 |
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| author | Guillot, Dominique Mashreghi, Javad Vishwakarma, Prateek Kumar |
| author_facet | Guillot, Dominique Mashreghi, Javad Vishwakarma, Prateek Kumar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21056 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Oppenheim--Schur inequalities for causal products Guillot, Dominique Mashreghi, Javad Vishwakarma, Prateek Kumar Functional Analysis Classical Analysis and ODEs 26D07, 15B48, 15A45, 15A15 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. |
| title | Oppenheim--Schur inequalities for causal products |
| topic | Functional Analysis Classical Analysis and ODEs 26D07, 15B48, 15A45, 15A15 |
| url | https://arxiv.org/abs/2602.21056 |