{"paper":{"title":"Counting dimensions of L-harmonic functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiaping Wang, Peter Li","submitted_at":"2000-09-01T00:00:00Z","abstract_excerpt":"In this article, we will consider second order uniformly elliptic operators of divergence form defined on R^n with measurable coefficients. Mainly, we will give estimates on the dimension of space of solutions that grow at most polynomially of degree d. More precisely, in terms of a rectangular coordinate system {x_1,...,x_n}, a second order uniformly elliptic operator of divergence form, L, acting on a function f in H^1_loc(R^n) is given by\n  Lf = sum_{ij} d/dx_i (a^{ij}(x) df/dx_j)\n  where (a^{ij}(x)) is an n x n symmetric matrix satisfying the ellipticity bounds\n  \\lambda I <= (a^{ij}) <= L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009254","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"}