{"paper":{"title":"Restriction of Fourier transforms to some complex curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jong-Guk Bak, Seheon Ham","submitted_at":"2011-11-28T11:19:26Z","abstract_excerpt":"The purpose of this paper is to prove a Fourier restriction estimate for certain 2-dimensional surfaces in $\\bbR^{2d}$, $d\\ge 3$. These surfaces are defined by a complex curve $\\gamma(z)$ of simple type, which is given by a mapping of the form % \\[ z\\mapsto \\gamma (z) = \\big(z, \\, z^2,..., \\, z^{d-1}, \\, \\phi(z) \\big) \\] % where $\\phi(z)$ is an analytic function on a domain $\\Omega \\subset \\bbC$. This is regarded as a real mapping $z=(x,y) \\mapsto \\gamma(x,y)$ from $\\Omega \\subset \\bbR^2$ to $\\bbR^{2d}$.\n  Our results cover the case $\\phi(z) = z^N$ for any nonnegative integer $N$, in all dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6409","kind":"arxiv","version":2},"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"}