{"title":"$$\\boldsymbol{H}^{mathbf{1}}{(\\mathbb{T})}$$ 中周期正交样条系统的非条件性：必然性","authors":"L. Hakobyan","doi":"10.3103/s1068362324700183","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We give a geometric characterization of knot sequences <span>\\((s_{n})\\)</span>, which is a necessary condition for the corresponding periodic orthonormal spline system of arbitrary order <span>\\(k\\)</span>, <span>\\(k\\in\\mathbb{N}\\)</span>, to be an unconditional basis in the atomic Hardy space on the torus <span>\\(H^{1}(\\mathbb{T})\\)</span>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unconditionality of Periodic Orthonormal Spline Systems in $$\\\\boldsymbol{H}^{\\\\mathbf{1}}{(\\\\mathbb{T})}$$ : Necessity\",\"authors\":\"L. Hakobyan\",\"doi\":\"10.3103/s1068362324700183\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>We give a geometric characterization of knot sequences <span>\\\\((s_{n})\\\\)</span>, which is a necessary condition for the corresponding periodic orthonormal spline system of arbitrary order <span>\\\\(k\\\\)</span>, <span>\\\\(k\\\\in\\\\mathbb{N}\\\\)</span>, to be an unconditional basis in the atomic Hardy space on the torus <span>\\\\(H^{1}(\\\\mathbb{T})\\\\)</span>.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3103/s1068362324700183\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3103/s1068362324700183","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Unconditionality of Periodic Orthonormal Spline Systems in $$\boldsymbol{H}^{\mathbf{1}}{(\mathbb{T})}$$ : Necessity
Abstract
We give a geometric characterization of knot sequences \((s_{n})\), which is a necessary condition for the corresponding periodic orthonormal spline system of arbitrary order \(k\), \(k\in\mathbb{N}\), to be an unconditional basis in the atomic Hardy space on the torus \(H^{1}(\mathbb{T})\).
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