Corpus ID: 235898963

A Tauberian Approach to an Analog of Weyl's law for the Kohn Laplacian on Compact Heisenberg Manifolds

@inproceedings{Fan2021ATA,
  title={A Tauberian Approach to an Analog of Weyl's law for the Kohn Laplacian on Compact Heisenberg Manifolds},
  author={Colin Fan and Elena Kim and Yunus E. Zeytuncu},
  year={2021}
}
Let M = Γ \ Hd be a compact quotient of the d-dimensional Heisenberg group Hd by a lattice subgroup Γ. We show that the eigenvalue counting function N(λ) for any fixed element of a family of second order differential operators {Lα} on M has asymptotic behavior N (λ) ∼ Cd,α vol (M)λ , where Cd,α is a constant that only depends on the dimension d and the parameter α. As a consequence, we obtain an analog of Weyl’s law (both on functions and forms) for the Kohn Laplacian on M . Our main tools are… Expand

References

SHOWING 1-9 OF 9 REFERENCES
Compact Heisenberg manifolds as CR manifolds
Let M be the quotient of the Heisenberg group by a discrete co-compact subgroup, with the natural strongly pseudoconvex CR structure. We identify the eigenvalues and eigenforms of the Kohn LaplaciansExpand
A Tauberian approach to Weyl’s law for the Kohn Laplacian on spheres
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 anExpand
Lp harmonic analysis and Radon transforms on the Heisenberg group
In this paper, harmonic analysis in the Heisenberg group Heisn = Cn × R with group law (z, t) · (z′, t′) = (z + z′, t + t′ − 12Im z · z′) is taken to mean the joint spectral theory of the operators LExpand
Spectral Asymptotics on Compact Heisenberg Manifolds
For $$M=\Gamma \backslash \mathbb {H}_d$$M=Γ\Hd a compact quotient of the real ($$2d+1$$2d+1)-dimensional Heisenberg group $$\mathbb {H}_d$$Hd by a lattice subgroup $$\Gamma $$Γ, we show that theExpand
Partial differential equations in several complex variables
This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last fewExpand
MASTER’S THESIS
Web mediated communications revolutionized traditional social interactions. It is designed to facilitate information exchange between individuals and to enable people to connect with friends, family,Expand
Wolfgang Peter
  • and Frank Steiner.Weyl’s Law: Spectral Properties of the Laplacian in Mathematics and Physics. John Wiley & Sons, Ltd,
  • 2009
The Heat Equation for the ∂ b – Laplacian
  • The Journal of Geometric Analysis
  • 2004
Noncommutative Harmonic Analysis. Number pt. 1 in Mathematical surveys and monographs
  • 1986