Discrete taut strings and real interpolation

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• 作者：Natan Kruglyak ^{natan.kruglyak@liu.se" class="auth_mail" title="E-mail the corresponding author} ; Eric Setterqvist ; ^{eric.setterqvist@liu.se" class="auth_mail" title="E-mail the corresponding author}
• 关键词：46E30 ; 46N10
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：270
• 期：2
• 页码：671-704
• 全文大小：572 K

文摘

Classical taut strings and their multidimensional generalizations appear in a broad range of applications. In this paper we suggest a general approach based on the K-functional of real interpolation that provides a unifying framework of existing theories and extend the range of applications of taut strings. More exactly, we introduce the notion of invariant K  -minimal sets, explain their connection to taut strings and characterize all bounded, closed and convex sets in 46&_mathId=si1.gif&_user=111111111&_pii=S0022123615004346&_rdoc=1&_issn=00221236&md5=17de9aa908f57a16648f7f4bdf85981d" title="Click to view the MathML source">Rⁿ${\mathbb{R}}^n$ that are invariant K  -minimal with respect to the couple 46&_mathId=si155.gif&_user=111111111&_pii=S0022123615004346&_rdoc=1&_issn=00221236&md5=4c5a56bd440b3730fef71df6cc77f420" title="Click to view the MathML source">(ℓ¹,ℓ^∞)$({\ell }^1,{\ell }^{\infty })$.