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A Tauberian approach to Weyl’s law for the Kohn Laplacian on spheres

Part of: CR manifolds

Published online by Cambridge University Press:  15 March 2021

Henry Bosch ,
Tyler Gonzales ,
Kamryn Spinelli ,
Gabe Udell  and
Yunus E. Zeytuncu
Henry Bosch
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA02138, USA e-mail: henrybosch@college.harvard.edu
Tyler Gonzales
Affiliation:
Department of Mathematics, University of Wisconsin–Eau Claire, Eau Claire, WI54701, USA e-mail: gonzaltj9215@uwec.edu
Kamryn Spinelli
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA01609, USA e-mail: kpspinelli@wpi.edu
Gabe Udell
Affiliation:
Department of Mathematics, Pomona College, Claremont, CA91711, USA e-mail: grua2017@mymail.pomona.edu
Yunus E. Zeytuncu*
Affiliation:
Department of Mathematics and Statistics, University of Michigan–Dearborn, Dearborn, MI48128, USA
*
e-mail: zeytuncu@umich.edu
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Abstract

We compute the leading coefficient in the asymptotic expansion of the eigenvalue counting function for the Kohn Laplacian on the spheres. We express the coefficient as an infinite sum and as an integral.

Keywords

Kohn LaplacianWeyl’s lawKaramata’s Tauberian Theorem

MSC classification

Primary: 32V05: CR structures, CR operators, and generalizations
Secondary: 32V20: Analysis on CR manifolds
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 134 - 154
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

This work is supported by NSF (DMS-1950102 and DMS-1659203). The work of the last author is also partially supported by a grant from the Simons Foundation (#353525).

References

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