Vol. 12, No. 5, 2019

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Spectra of Kohn Laplacians on spheres

John Ahn, Mohit Bansil, Garrett Brown, Emilee Cardin and Yunus E. Zeytuncu

Vol. 12 (2019), No. 5, 855–869
Abstract

We study the spectrum of the Kohn Laplacian on the unit spheres in n and revisit Folland’s classical eigenvalue computation. We also look at the growth rate of the eigenvalue counting function in this context. Finally, we consider the growth rate of the eigenvalues of the perturbed Kohn Laplacian on the Rossi sphere in 2 .

Keywords
Kohn Laplacian, spherical harmonics, Gershgorin's circle theorem
Mathematical Subject Classification 2010
Primary: 32V05
Secondary: 32V30
Milestones
Received: 5 September 2018
Accepted: 26 December 2018
Published: 22 May 2019
Authors
John Ahn
Bowdoin College
Brunswick, ME
United States
Mohit Bansil
Michigan State University
East Lansing, MI
United States
Garrett Brown
Harvard University
Cambridge, MA
United States
Emilee Cardin
College of William and Mary
Williamsburg, VA
United States
Yunus E. Zeytuncu
Department of Mathematics and Statistics
University of Michigan-Dearborn
Dearborn, MI
United States