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Smooth Orthogonal Projections on Riemannian Manifold

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Abstract

We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const. Approx., 41, 23–48 2015).

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, 97403–1222, USA

    Marcin Bownik

  2. Faculty of Applied Mathematics, Gdańsk University of Technology, ul. G. Narutowicza 11/12, 80-952, Gdańsk, Poland

    Karol Dziedziul

  3. Institute of Mathematics, Polish Academy of Sciences, ul. Abrahama 18, 81-825, Sopot, Poland

    Anna Kamont

Authors
  1. Marcin Bownik
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  2. Karol Dziedziul
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  3. Anna Kamont
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Correspondence to Marcin Bownik.

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Most of the paper was written during the academic year 2016/17 when the first author was visiting the Institute of Mathematics of the Polish Academy of Sciences. The authors would like to thank Institute of Mathematics of the Polish Academy of Sciences for this support. The first author was partially supported by the NSF grant DMS-1665056 and by a grant from the Simons Foundation #426295.

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Bownik, M., Dziedziul, K. & Kamont, A. Smooth Orthogonal Projections on Riemannian Manifold. Potential Anal 54, 41–94 (2021). https://doi.org/10.1007/s11118-019-09818-3

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  • DOI: https://doi.org/10.1007/s11118-019-09818-3

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