{"paper":{"title":"Functions operating on modulation spaces and nonlinear dispersive equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Divyang G. Bhimani, P. K. Ratnakumar","submitted_at":"2014-12-01T06:57:45Z","abstract_excerpt":"The aim of this paper is two fold. We show that if a complex function $F$ on $\\C$ operates in the modulation spaces $M^{p,1}(\\R^n)$ by composition, then $F$ is real analytic on $\\R^2 \\approx \\C$. This answers negatively, the open question posed in [M. Ruzhansky, M. Sugimoto, B. Wang, Modulation Spaces and Nonlinear Evolution Equations, arXiv:1203.4651], regarding the general power type nonlinearity of the form $|u|^\\alpha u$. We also characterise the functions that operate in the modulation space $M^{1,1}(\\R^n)$.\n  The local well-posedness of the NLS, NLW and NLKG equations for the `real entir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0362","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"}