Finiteness Principles for Smooth Selection |
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| Authors: | Charles Fefferman Arie Israel Garving K Luli |
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| Institution: | 1.Department of Mathematics,Princeton University,Princeton,USA;2.Department of Mathematics,The University of Texas at Austin,Austin,USA;3.Department of Mathematics,University of California, Davis,Davis,USA |
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| Abstract: | In this paper we prove finiteness principles for \({C^m{({\mathbb{R}^n},{\mathbb{R}^D)}}}\) and \({C^{m-1,1}(\mathbb{R}^n,\mathbb{R}^D)}\) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is \({X=\mathbb{R}^n}\). |
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