Sharp Spectral Asymptotics for Dirac Energy

2007/08/29 by Ivrii, Victor
#35P20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.0708.3934

Abstract

I derive sharp semiclassical asymptotics of ∫ |e_h(x,y,0)|²ω(x,y) dx dy where e_h(x,y,τ) is the Schwartz kernel of the spectral projector and ω(x,y) is singular as x=y. I also consider asymptotics of more general expressions.

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