{"paper":{"title":"Spectral property of self-affine measures on ${\\mathbb R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Jing-Cheng Liu, Jun Jason Luo","submitted_at":"2016-03-19T12:03:49Z","abstract_excerpt":"We study spectral properties of the self-affine measure $\\mu_{M,\\mathcal {D}}$ generated by an expanding integer matrix $M\\in M_n(\\mathbb{Z})$ and a consecutive collinear digit set $\\mathcal {D}=\\{0,1,\\dots,q-1\\}v$ where $v\\in \\mathbb{Z}^n\\setminus\\{0\\}$ and $q\\ge 2$ is an integer. Some sufficient conditions for $\\mu_{M,\\mathcal {D}}$ to be a spectral measure or to have infinitely many orthogonal exponentials are given. Moreover, for some special cases, we can obtain a necessary and sufficient condition on the spectrality of $\\mu_{M,\\mathcal {D}}$. Our study generalizes the one dimensional res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07656","kind":"arxiv","version":2},"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"}