{"paper":{"title":"Regularization of an autoconvolution problem in ultrashort laser pulse characterization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.optics"],"primary_cat":"math-ph","authors_text":"Bernd Hofmann, Daniel Gerth, G\\\"unter Steinmeyer, Sebastian Koke, Simon Birkholz","submitted_at":"2013-01-25T15:14:20Z","abstract_excerpt":"An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically required extension of the deautoconvolution problem beyond the classical case usually discussed in literature: (i) For measurements of ultrashort laser pulses with the self-diffraction SPIDER method, a stable approximate solution of an autocovolution equation with a complex-valued kernel function is needed. (ii) The considered scenario requires complex funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6061","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":""},"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"}