Abstract
Section 9.1 presents the Yu. Brudnyi and Shvartsman criteria characterizing the trace spaces for Lipschitz functions of higher order and those for the associated jet spaces. Their proofs widely exploit the concepts and methods of Local Approximation Theory. In particular, the key tools are the Yu. Brudnyi inequality relating local approximation to the corresponding di_erence characteristic, see Volume I, Theorem 2.37, and a Whitney type extension construction with Taylor polynomials replaced by polynomials of the best local approximation.
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© 2012 Springer Basel AG
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Brudnyi, A., Brudnyi, Y. (2012). Traces to Closed Subsets:Criteria, Applications. In: Methods of Geometric Analysis in Extension and Trace Problems. Monographs in Mathematics, vol 103. Springer, Basel. https://doi.org/10.1007/978-3-0348-0212-3_4
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DOI: https://doi.org/10.1007/978-3-0348-0212-3_4
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0211-6
Online ISBN: 978-3-0348-0212-3
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