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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17564609 |
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| _version_ | 1866901471560204288 |
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| author | Kawasaki, Hideyo |
| author_facet | Kawasaki, Hideyo |
| contents | <p>A renormalized analytic correspondence between Fredholm determinants and Hermite–Biehler entire functions is established within the **Conservative Motion Theory (CMT)** framework. <br>For $\kappa>0$, a Gaussian reflection–positive operator defines $\Xi_\kappa(E)=\det_2(I-\alpha K_\kappa(E))$ with real, simple zeros. <br>Through torus compactification and Szegő–Widom renormalization, the limit $\kappa\!\to\!0^{+}$ defines $\Xi_0(E)$, preserving real–zero structure under a uniform Hermite–Biehler limit. <br>The coupling $\alpha=1/(2\pi)$ is uniquely determined via Mellin analysis, providing an analytic completion of the Fredholm–de Branges correspondence and a rigorous foundation for real–zero persistence in analytic number theory.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17564609 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Conservative Motion Theory II: Analytic Completion of the Fredholm–de Branges Correspondence Kawasaki, Hideyo <p>A renormalized analytic correspondence between Fredholm determinants and Hermite–Biehler entire functions is established within the **Conservative Motion Theory (CMT)** framework. <br>For $\kappa>0$, a Gaussian reflection–positive operator defines $\Xi_\kappa(E)=\det_2(I-\alpha K_\kappa(E))$ with real, simple zeros. <br>Through torus compactification and Szegő–Widom renormalization, the limit $\kappa\!\to\!0^{+}$ defines $\Xi_0(E)$, preserving real–zero structure under a uniform Hermite–Biehler limit. <br>The coupling $\alpha=1/(2\pi)$ is uniquely determined via Mellin analysis, providing an analytic completion of the Fredholm–de Branges correspondence and a rigorous foundation for real–zero persistence in analytic number theory.</p> |
| title | Conservative Motion Theory II: Analytic Completion of the Fredholm–de Branges Correspondence |
| url | https://doi.org/10.5281/zenodo.17564609 |