{"paper":{"title":"On N\\\"orlund summation and Ergodic Theory, with applications to power series of Hilbert contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christophe Cuny, Michel Weber","submitted_at":"2017-07-01T07:07:31Z","abstract_excerpt":"We show that if ${\\bf a}=(a_n)_{n\\in \\N}$ is a good weight for the dominated weighted ergodic theorem in $L^p$, $p>1$, then the N\\\"orlund matrix $N_{\\bf a}=\\{a_{i-j}/A_i\\}_{0\\le j\\le i}$, $A_i=\\sum_{k=0}^i |a_k|$ is bounded on $\\ell^p(\\N)$. We study the regularity (convergence in norm, almost everywhere) of operators in ergodic theory: power series of Hilbert contractions, and power series $\\sum_{n\\in \\N} a_nP_nf $ of $L^2$-contractions, and establish similar tight relations with the N\\\"orlund operator associated to the modulus coefficient sequence $(|a_n|)_{n\\in \\N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00104","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"}