Abstract
We present an explicit formula for the leading coefficient in the asymptotic expansion of the eigenvalue counting function of the Kohn Laplacian on the unit sphere \({\mathbb {S}}^{2n-1}\).
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Notes
For more information on spherical harmonics we refer to [12]. We simplify the notation by writing just \({\mathcal {H}}_{p,q}\).
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Acknowledgements
We would like to thank the anonymous referee for constructive feedback. We would like to thank Siqi Fu and Tommie Reerink for careful comments on an earlier version of this paper. This research was partially conducted at the NSF REU Site (DMS-1659203) in Mathematical Analysis and Applications at the University of Michigan-Dearborn. We would like to thank the National Science Foundation, National Security Agency, and University of Michigan-Dearborn for their support.
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This work is supported by NSF (DMS-1659203). The work of the second author is also partially supported by a grant from the Simons Foundation (#353525).
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Bansil, M., Zeytuncu, Y.E. An analog of the Weyl law for the Kohn Laplacian on spheres. Complex Anal Synerg 6, 1 (2020). https://doi.org/10.1007/s40627-019-0038-0
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DOI: https://doi.org/10.1007/s40627-019-0038-0