{"paper":{"title":"Stechkin's problem for functions of a self-adjoint operator in a Hilbert space, Taikov-type inequalities and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nadiia Kriachko, Vladyslav Babenko, Yuliya Babenko","submitted_at":"2017-03-11T23:53:41Z","abstract_excerpt":"In this paper we solve the problem of approximating functionals $(\\varphi(A)x, f)$ (where $\\varphi(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another function $\\psi (A)$ of the operator $A$. In addition, we obtain a series of sharp Taikov-type additive inequalities that estimate $|(\\varphi(A)x, f)|$ with the help of $\\| \\psi (A)x\\|$ and $\\| x\\|$. We also present several applications of the obtained results. First, we find sharp constants in inequalities of the type used in H${\\rm{\\ddot{o}}}$rmander theorem on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04045","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"}