{"paper":{"title":"Equiconvergence of spectral decompositions of Hill-Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Boris Mityagin, Plamen Djakov","submitted_at":"2011-10-31T05:28:40Z","abstract_excerpt":"We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator $L= -d^2/dx^2 + v(x), $ $x \\in [0,\\pi], $ with $H_{per}^{-1} $-potential and the free operator $L^0=-d^2/dx^2, $ subject to periodic, antiperiodic or Dirichlet boundary conditions.\n  In particular, we prove that $$ \\|S_N - S_N^0: L^a \\to L^b \\| \\to 0 \\quad \\text{if} \\;\\; 1<a \\leq b< \\infty, \\;\\; 1/a - 1/b <1/2, $$ where $S_N$ and $S_N^0 $ are the $N$-th partial sums of the spectral decompositions of $L$ and $L^0.$ Moreover, if $v \\in H^{-\\alpha} $ with $1/2 < \\alpha < 1$ and $\\frac{1}{a}=("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6696","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"}