Curvature–Spectrum Rigidity for Positive Laplace Transforms A Complete Inverse Classification Theorem
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866901942802841600 |
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| author | Chaudhary, Abhishek |
| author_facet | Chaudhary, Abhishek |
| contents | <p>This paper develops a second-order rigidity theory for positive Laplace transforms of finite measures. It proves that the long-time behavior of the curvature of the logarithm of a Laplace transform completely determines the geometric structure of the boundary spectrum of the underlying measure. Specifically, the paper shows that curvature collapse to zero occurs if and only if the boundary spectrum consists of a single point, while persistent curvature indicates multiple competing boundary modes. It further establishes a sharp necessary and sufficient condition—formulated as a boundary thickness criterion—for exponential curvature decay, which is equivalent to the presence of a spectral gap. The results provide a full two-sided classification linking second-derivative asymptotics to spectral geometry, without requiring analytic continuation or complex analytic techniques. Conceptually, the work promotes curvature to a second-order Tauberian invariant and shows that spectral multiplicity and rigidity can be recovered purely from variance behavior under exponential tilting.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18743415 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Curvature–Spectrum Rigidity for Positive Laplace Transforms A Complete Inverse Classification Theorem Chaudhary, Abhishek Laplace transform Spectral rigidity Tauberian theory Spectral gap Boundary spectrum Exponential asymptotic s Inverse spectral theory Asymptotic analysis Functional analysis Inverse spectral theory Asymptotic analysis Functional analysis <p>This paper develops a second-order rigidity theory for positive Laplace transforms of finite measures. It proves that the long-time behavior of the curvature of the logarithm of a Laplace transform completely determines the geometric structure of the boundary spectrum of the underlying measure. Specifically, the paper shows that curvature collapse to zero occurs if and only if the boundary spectrum consists of a single point, while persistent curvature indicates multiple competing boundary modes. It further establishes a sharp necessary and sufficient condition—formulated as a boundary thickness criterion—for exponential curvature decay, which is equivalent to the presence of a spectral gap. The results provide a full two-sided classification linking second-derivative asymptotics to spectral geometry, without requiring analytic continuation or complex analytic techniques. Conceptually, the work promotes curvature to a second-order Tauberian invariant and shows that spectral multiplicity and rigidity can be recovered purely from variance behavior under exponential tilting.</p> |
| title | Curvature–Spectrum Rigidity for Positive Laplace Transforms A Complete Inverse Classification Theorem |
| topic | Laplace transform Spectral rigidity Tauberian theory Spectral gap Boundary spectrum Exponential asymptotic s Inverse spectral theory Asymptotic analysis Functional analysis Inverse spectral theory Asymptotic analysis Functional analysis |
| url | https://doi.org/10.5281/zenodo.18743415 |