{"paper":{"title":"A Simplified Calculation for the Fundamental Solution to the Heat Equation on the Heisenberg Group","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Boggess, Andrew Raich","submitted_at":"2007-11-26T21:03:40Z","abstract_excerpt":"Let $L = -1/4 (\\sum_{j=1}^n(X_j^2+Y_j^2)+i\\gamma T)$ where $\\gamma$ is a complex number, $X_j$, $Y_j$, and $T$ are the left invariant vector fields of the Heisenberg group structure for $R^n \\times R^n \\times R$. We explicitly compute the Fourier transform (in the spatial variables) of the fundamental solution of the Heat Equation $\\partial_s\\rho = -L\\rho$. As a consequence, we have a simplified computation of the Fourier transform of the fundamental solution of the $\\Box_b$-heat equation on the Heisenberg group and an explicit kernel of the heat equation associated to the weighted dbar-operat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.4117","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"}