{"id":"openai-math/Endpoint-convergence-for-the-planar-Schrodinger-equation","pdf":"https://github.com/openai/math/blob/main/preprints/Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026","tags":["harmonic-analysis","schrodinger-equation","pointwise-convergence"],"score":0,"title":"Endpoint convergence for the planar Schrodinger equation","domain":"Real and complex analysis","family":"080","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We resolve the planar Sobolev endpoint of Carleson's convergence problem: for initial data in $`H^{1/3}(\\mathbb R^2)`$, the Schrödinger evolution converges almost everywhere to the initial data as $`t\\downarrow0`$. The evolution is defined by taking the Gaussian regularization limit first; on one full-measure spatial set, this limit exists for every $`0\\lt t\\lt 1`$, and the resulting evolution is continuous at t = 0.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The exact Sobolev endpoint for Schrödinger convergence"}