New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In addition, an extension theorem for valuations defined on functions with lower dimensional domain is proved, and its connection to the Abel transform is explained. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
The Hadwiger theorem on convex functions, IV: The Klain approach / Andrea Colesanti; Monika Ludwig; Fabian Mussnig. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - ELETTRONICO. - 413:(2023), pp. 0-0. [10.1016/j.aim.2022.108832]
The Hadwiger theorem on convex functions, IV: The Klain approach
Andrea Colesanti;Fabian Mussnig
2023
Abstract
New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In addition, an extension theorem for valuations defined on functions with lower dimensional domain is proved, and its connection to the Abel transform is explained. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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