A note on D-functions and P-covariances on Hilbert spaces and related inequalities
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912458738761728 |
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| author | Scarlatti, Sergio |
| author_facet | Scarlatti, Sergio |
| contents | In this note we first review the concept of D-function, closely connected with Cauchy-Schwarz inequality, and then introduce the notion of P-covariance on a Hilbert space, where $P$ is an orthogonal projection. We show that when P is specialized to be one-dimensional many well-known inequalities such as Buzano, Richard and Walker inequalities are simple consequences of P-covariance inequalities and their relation with D-functions. By means of these concepts enhancements of the previous mentioned inequalities are also established with minimum effort. A more thorough analysis of Walker inequality is presented jointly with some novel financial considerations as well as a new refinement of Holder inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on D-functions and P-covariances on Hilbert spaces and related inequalities Scarlatti, Sergio General Mathematics In this note we first review the concept of D-function, closely connected with Cauchy-Schwarz inequality, and then introduce the notion of P-covariance on a Hilbert space, where $P$ is an orthogonal projection. We show that when P is specialized to be one-dimensional many well-known inequalities such as Buzano, Richard and Walker inequalities are simple consequences of P-covariance inequalities and their relation with D-functions. By means of these concepts enhancements of the previous mentioned inequalities are also established with minimum effort. A more thorough analysis of Walker inequality is presented jointly with some novel financial considerations as well as a new refinement of Holder inequality. |
| title | A note on D-functions and P-covariances on Hilbert spaces and related inequalities |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2507.00009 |