{"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}
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Abstract
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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