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Another Way to Look at Spectral Asymptotics on Spheres

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Abstract

The exact spectrum of the Laplacian on spheres is well-known, and produces a relatively large remainder in the Weyl asymptotic formula. We observe that we can obtain an exact asymptotic formula with no remainder if we take a finite sum of terms involving powers and periodic functions.

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Notes

  1. Using the usual notation that \([s]\) is the integral part of \(s\) and \(\langle s\rangle \) is the fractional part of \(s\).

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Acknowledgments

Robert S. Strichartz supported by the National Science Foundation grant DMS-1162045.

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Authors and Affiliations

  1. Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY, 14853, USA

    Robert S. Strichartz

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  1. Robert S. Strichartz
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Correspondence to Robert S. Strichartz.

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Communicated by Hans G. Feichtinger.

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Strichartz, R.S. Another Way to Look at Spectral Asymptotics on Spheres. J Fourier Anal Appl 21, 401–404 (2015). https://doi.org/10.1007/s00041-014-9377-7

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  • DOI: https://doi.org/10.1007/s00041-014-9377-7

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