{"title":"凸函数的哈德维格定理，I","authors":"Andrea Colesanti, Monika Ludwig, Fabian Mussnig","doi":"10.1007/s00039-024-00693-8","DOIUrl":null,"url":null,"abstract":"<p>A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on <span>\\({\\mathbb{R}}^{n}\\)</span> is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Hadwiger Theorem on Convex Functions, I\",\"authors\":\"Andrea Colesanti, Monika Ludwig, Fabian Mussnig\",\"doi\":\"10.1007/s00039-024-00693-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on <span>\\\\({\\\\mathbb{R}}^{n}\\\\)</span> is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00039-024-00693-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00039-024-00693-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on \({\mathbb{R}}^{n}\) is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.
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