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A proof of the Calderon extension theorem

Marsden, J. (1973) A proof of the Calderon extension theorem. Canadian Mathematical Bulletin, 16 (1). pp. 133-136. ISSN 0008-4395.

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In this note we outline a proof of the Calderon extension theorem by a technique similar to that for the Whitney extension theorem. For classical proofs, see Calderon [2] and Morrey [4]. See also Palais [6, p. 170]. Our purpose is thus to give am ore unified proof of the theorem in the various cases. In addition, the proof applies to the Holder space C^(k+a), which was used in [3], and applied to regions satisfying the "cone condition" of Calderon. Let M be a compact C^∞ manifold with C^∞ boundary embedded as an open submanifold of a compact manifold M. Let π:E→M be a vector bundle and let L:^p_k(π), L:^p_k(π ׀ M) be the usual Sobolev spaces and H^k=L:^2_k. See [2], [5],or [6] for the definitions. Here, denotes restriction. We prove the following for H^8 (s≥O an integer), but a similar proof also holds for L≥p_k:, and C^(k+a), 0≤1X≤1.

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Additional Information:© 1973 CMS. Partially supported by National Research Council of Canada and NSF Grant GP-l5735.
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ID Code:19638
Deposited By: Ruth Sustaita
Deposited On:01 Sep 2010 21:41
Last Modified:03 Oct 2019 01:59

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