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
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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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