{"paper":{"title":"Isometries of $L_p$-spaces of solutions of homogeneous partial differential equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander Koldobsky","submitted_at":"1993-12-15T16:07:01Z","abstract_excerpt":"Let $ n\\geq 2, A=(a_{ij})_{i,j=1}^{n}$ be a real symmetric matrix, $a=(a_i)_{i=1}^{n}\\in \\Bbb R^n.$ Consider the differential operator $D_A = \\sum_{i,j=1}^n a_{ij}{\\partial^2 \\over \\partial x_i \\partial x_j}+ \\sum_{i=1}^n a_i{\\partial \\over \\partial x_i}.$ Let $E$ be a bounded domain in $\\Bbb R^n,$ $p>0.$ Denote by $L_{D_A}^p(E)$ the space of solutions of the equation $D_A f=0$ in the domain $E$ provided with the $L_p$-norm.\n  We prove that, for matrices $A,B,$ vectors $a,b,$ bounded domains $E,F,$ and every $p>0$ which is not an even integer, the space $L_{D_A}^p(E)$ is isometric to a subspac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9312205","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"}