@inproceedings{d2cf3a3dd0c443408ecb5e78b99ae3c2,

title = "Pointwise weyl law for partial bergman kernels",

abstract = " 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 K{\"a}hler manifold. The first result is a complete asymptotic expansion for smoothed spectral projections in terms of periodic orbit data. When the orbit is {\textquoteleft}strongly hyperbolic{\textquoteright} 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. ",

author = "Steve Zelditch and Peng Zhou",

note = "Funding Information: Research partially supported by NSF grant and DMS-1541126 and by the Stefan Bergman trust. Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.; Workshop on Algebraic and Analytic Microlocal Analysis, AAMA 2013 ; Conference date: 20-05-2013 Through 24-05-2013",

year = "2018",

doi = "10.1007/978-3-030-01588-6_13",

language = "English (US)",

isbn = "9783030015862",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "589--634",

editor = "Michael Hitrik and Dmitry Tamarkin and Boris Tsygan and Steve Zelditch",

booktitle = "Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013",

}