{"paper":{"title":"Some properties of block-radial functions and Schr\\\"odinger type operators with block-radial potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alicja Dota, Leszek Skrzypczak","submitted_at":"2018-09-04T08:35:37Z","abstract_excerpt":"Let $ R_\\gamma B^{s}_{p,q}(\\Rd)$ be a subspace of the Besov space $B^{s}_{p,q}(\\Rd)$ that consists of block-radial functions. We prove that the asymptotic behaviour of the entropy numbers of compact embeddings $\\id: \\: R_\\gamma B^{s_1}_{p_1,q_1}(\\R^d) \\rightarrow R_\\gamma B^{s_2}_{p_2,q_2}(\\R^d)$ depends on the number of blocks of the lowest dimension, the parameters $p_1$ and $p_2$, but is independent of the smoothness parameters $s_1$, $s_2$. We apply the asymptotic behaviour to estimation of powers of a negative spectra of Schr\\\"odinger type operators with block-radial potentials. This part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00833","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"}