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Continuous Solutions of Linear Equations

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From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Part of the book series: Developments in Mathematics ((DEVM,volume 28))

Abstract

We provide necessary and sufficient conditions for existence of continuous solutions of a system of linear equations whose coefficients are continuous functions.

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Acknowledgements

We thank M. Hochster for communicating his unpublished example (3.4). We are grateful to B. Klartag and A. Naor for bringing Michael’s theorem to our attention at a workshop organized by the American Institute of Mathematics (AIM), to which we are also grateful. Our earlier proof of (6) was unnecessarily complicated. We thank H. Brenner, A. Isarel, K. Luli, R. Narasimhan, A. Némethi, and T. Szamuely for helpful conversations and F. Wroblewski for TeXing several sections of this chapter.

Partial financial support for CF was provided by the NSF under grant number DMS-0901040 and by the ONR under grant number N00014-08-1-0678. Partial financial support for JK was provided by the NSF under grant number DMS-0758275.

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Authors and Affiliations

  1. Princeton University, Princeton, NJ, 08544-1000, USA

    Charles Fefferman & János Kollár

Authors
  1. Charles Fefferman
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  2. János Kollár
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Corresponding author

Correspondence to Charles Fefferman .

Editor information

Editors and Affiliations

  1. , Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Hershel M. Farkas

  2. , Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, 08544, New Jersey, USA

    Robert C. Gunning

  3. , Department of Mathematics, Temple University, Wachman Hall 608, Philadelphia, 19122, Pennsylvania, USA

    Marvin I. Knopp

  4. , Department of Mathematics, University of Michigan, Church St. 530, Ann Arbor, 48109, Michigan, USA

    B. A. Taylor

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Fefferman, C., Kollár, J. (2013). Continuous Solutions of Linear Equations. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_10

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