Pointwise weyl law for partial bergman kernels

Steve Zelditch*, Peng Zhou

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


This article is a continuation of a series by the authors on partial Bergman kernels and their asymptotic expasions. We prove a 2-term pointwise Weyl law for semi-classical spectral projections onto sums of eigenspaces of spectral width ħ = k -1 of Toeplitz quantizations (Formula presented) of Hamiltonians on powers L k of a positive Hermitian holomorphic line bundle L → M over a Kähler manifold. The first result is a complete asymptotic expansion for smoothed spectral projections in terms of periodic orbit data. When the orbit is ‘strongly hyperbolic’ the leading coefficient defines a uniformly continuous measure on R and a semi-classical Tauberian theorem implies the 2-term expansion. As in previous works in the series, we use scaling asymptotics of the Boutet-de-Monvel–Sjostrand parametrix and Taylor expansions to reduce the proof to the Bargmann–Fock case.

Original languageEnglish (US)
Title of host publicationAlgebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013
EditorsMichael Hitrik, Dmitry Tamarkin, Boris Tsygan, Steve Zelditch
PublisherSpringer New York LLC
Number of pages46
ISBN (Print)9783030015862
StatePublished - 2018
EventWorkshop on Algebraic and Analytic Microlocal Analysis, AAMA 2013 - Evanston, United States
Duration: May 20 2013May 24 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


OtherWorkshop on Algebraic and Analytic Microlocal Analysis, AAMA 2013
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Mathematics(all)


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