{"paper":{"title":"On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.MG","authors_text":"Krzysztof Baranski","submitted_at":"2011-05-25T08:04:30Z","abstract_excerpt":"We determine the Hausdorff and box dimension of the fractal graphs for a general class of Weierstrass-type functions of the form $f(x) = \\sum_{n=1}^\\infty a_n \\, g(b_n x + \\theta_n)$, where $g$ is a periodic Lipschitz real function and $a_{n+1}/a_n \\to 0$, $b_{n+1}/b_n \\to \\infty$ as $n \\to \\infty$. Moreover, for any $H, B \\in [1, 2]$, $H \\leq B$ we provide examples of such functions with $\\dim_H(\\graph f) = \\underline{\\dim}_B(\\graph f) = H$, $\\bar{\\dim}_B(\\graph f) = B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4960","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"}