{"paper":{"title":"Kramers-Kronig relations via Laplace formalism and $L^1$ integrability","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alessio Perinelli, Leonardo Ricci, Marco Prevedelli","submitted_at":"2024-07-31T15:39:12Z","abstract_excerpt":"Kramers-Kronig relations link the real and imaginary part of the Fourier transform of a well-behaved causal transfer function describing a linear, time-invariant system. From the physical point of view, according to the Kramers-Kronig relations, absorption and dispersion become two sides of the same coin. Due to the simplicity of the assumptions underlying them, the relations are a cornerstone of physics. The rigorous mathematical proof was carried out by Titchmarsh in 1937 and just requires the transfer function to be square-integrable ($L^2$), or equivalently that the impulse response of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.21694","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.21694/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}