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- W4213233429 abstract "Let (M= Gamma setminus mathbb {H}_d) be a compact quotient of the d-dimensional Heisenberg group (mathbb {H}_d) by a lattice subgroup (Gamma ). We show that the eigenvalue counting function (N^alpha left( lambda right) ) for any fixed element of a family of second order differential operators (left{ mathcal {L}_alpha right} ) on M has asymptotic behavior (N^alpha left( lambda right) sim C_{d,alpha } {text {vol}}left( Mright) lambda ^{d + 1}), where (C_{d,alpha }) is a constant that only depends on the dimension d and the parameter (alpha ). 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 Folland’s description of the spectrum of ({mathcal {L}}_{alpha }) and Karamata’s Tauberian theorem." @default.
- W4213233429 created "2022-02-24" @default.
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- W4213233429 date "2022-02-14" @default.
- W4213233429 modified "2023-10-08" @default.
- W4213233429 title "A Tauberian approach to an analog of Weyl’s law for the Kohn Laplacian on compact Heisenberg manifolds" @default.
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- W4213233429 doi "https://doi.org/10.1007/s40627-022-00094-3" @default.
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