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2025
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| Accès en ligne: | https://doi.org/10.5281/zenodo.17854877 |
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| _version_ | 1866901471386140672 |
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| author | Kawasaki, Hideyo |
| author_facet | Kawasaki, Hideyo |
| contents | <p>In Conservative Motion Theory I (CMT I) we constructed a reflection–positive Fredholm<br>kernel Kκ whose associated Fredholm determinant Ξκ admits a de Branges representation<br>and whose κ → 0+ limit Ξ0 satisfies a real–zero persistence principle. The aim of this<br>second part is to complete the analytic Fredholm–de Branges correspondence and to close<br>the remaining gaps between the operator–theoretic Fredholm framework and the classical de<br>Branges theory of Hilbert spaces of entire functions.<br>We construct a canonical family of de Branges spaces H(Eκ) associated with Kκ and prove<br>that the following four conditions hold in the CMT framework: (G1) uniform exchange and<br>boundary control of the Fredholm determinant, (G2) global Hilbert–Biehler (HB) positivity and<br>its κ → 0+ continuity, (G3) non–circularity of the critical strip and analytic determination of<br>the phase parameter α, and (G4) a sharp Phragmén–Lindelöf closure which forces the canonical<br>H–function to be H(E) = 1. Together, these conditions yield the analytic completion of the<br>Fredholm–de Branges correspondence for the CMT kernel, in the sense that the limiting de<br>Branges space is uniquely determined and carries the full zero–set information of the limiting<br>Fredholm determinant.<br>The Appendix provides a detailed analysis of HB positivity continuity and Phragmén–<br>Lindelöf closure (Appendix A), as well as technical complements on de Branges spaces,<br>non–circularity, trace asymptotics and Mellin normalization (Appendices B–F). Throughout<br>the paper we work with a fixed reflection–positive Fredholm kernel and do not invoke any<br>external numerical input: all zero–set and growth information is encoded analytically in the<br>Conservative Motion Theory framework.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17854877 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | Conservative Motion Theory II: Analytic Completion of the Fredholm–de Branges Correspondence Kawasaki, Hideyo <p>In Conservative Motion Theory I (CMT I) we constructed a reflection–positive Fredholm<br>kernel Kκ whose associated Fredholm determinant Ξκ admits a de Branges representation<br>and whose κ → 0+ limit Ξ0 satisfies a real–zero persistence principle. The aim of this<br>second part is to complete the analytic Fredholm–de Branges correspondence and to close<br>the remaining gaps between the operator–theoretic Fredholm framework and the classical de<br>Branges theory of Hilbert spaces of entire functions.<br>We construct a canonical family of de Branges spaces H(Eκ) associated with Kκ and prove<br>that the following four conditions hold in the CMT framework: (G1) uniform exchange and<br>boundary control of the Fredholm determinant, (G2) global Hilbert–Biehler (HB) positivity and<br>its κ → 0+ continuity, (G3) non–circularity of the critical strip and analytic determination of<br>the phase parameter α, and (G4) a sharp Phragmén–Lindelöf closure which forces the canonical<br>H–function to be H(E) = 1. Together, these conditions yield the analytic completion of the<br>Fredholm–de Branges correspondence for the CMT kernel, in the sense that the limiting de<br>Branges space is uniquely determined and carries the full zero–set information of the limiting<br>Fredholm determinant.<br>The Appendix provides a detailed analysis of HB positivity continuity and Phragmén–<br>Lindelöf closure (Appendix A), as well as technical complements on de Branges spaces,<br>non–circularity, trace asymptotics and Mellin normalization (Appendices B–F). Throughout<br>the paper we work with a fixed reflection–positive Fredholm kernel and do not invoke any<br>external numerical input: all zero–set and growth information is encoded analytically in the<br>Conservative Motion Theory framework.</p> |
| title | Conservative Motion Theory II: Analytic Completion of the Fredholm–de Branges Correspondence |
| url | https://doi.org/10.5281/zenodo.17854877 |