{"paper":{"title":"On the dimension of divergence sets of Schr\\\"odinger equation with complex time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiqiang Zheng, Jiye Yuan, Tengfei Zhao","submitted_at":"2019-11-20T00:41:09Z","abstract_excerpt":"This article studies the pointwise convergence for the fractional Schr\\\"odinger operator $P^{t}_{a,\\gamma}$ with complex time in one spatial dimension. Through establishing $L^2$-maximal estimates for initial datum in $H^{s}(\\mathbb{R})$, we see that the solution converges to the initial data almost everywhere with $s>\\frac14 a(1-\\frac1\\gamma)_+$ when $0<a<1$ and $s>\\frac{1}{2}(1-\\frac{1}{\\gamma})_{+}$ when $a=1$. By constructing counterexamples, we show that this result is almost sharp up to the endpoint. These results extends the results of P. Sj\\\"olin, F. Soria and A. Baily. Second, we stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.08643","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/1911.08643/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"}