{"id":"openai-math/Endpoint-pointwise-convergence-for-the-Schrodinger-equation-in-higher-dimensions","pdf":"https://github.com/openai/math/blob/main/preprints/Endpoint-pointwise-convergence-for-the-Schrodinger-equation-in-higher-dimensions-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Endpoint-pointwise-convergence-for-the-Schrodinger-equation-in-higher-dimensions-September-24-2026","tags":["harmonic-analysis","schrodinger-equation","pointwise-convergence"],"score":0,"title":"Endpoint pointwise convergence for the Schrodinger equation in higher dimensions","domain":"Real and complex analysis","family":"080","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We resolve the Sobolev endpoint of Carleson's pointwise convergence problem in every dimension n ≥ 3. For initial data in $`H^{n/(2(n+1))}(\\mathbb R^n)`$, the free Schrödinger evolution converges almost everywhere to the initial data as $`t\\downarrow0`$. The evolution is defined by removing Gaussian regularization on one full-measure spatial set, uniformly over the interval $`0\\lt t\\lt 1`$.","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"}