I derive sharp semiclassical asymptotics of \(\int {|e_h } \left( {x,y,0} \right)|^2 \omega \left( {x,y} \right)dxdy\) 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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Bronstein, M., Ivrii, V.: Sharp Spectral Asymptotics for Operators with Irregular coefficients. Pushing the limits. Commun. Partial Differ. Equ. 28, no. 1–2, 99–123 (2003)
Ivrii, V.: Semiclassical asymptotics for exchange energy. Séminaire sur les Équations aux Dérivées Partielles, 1993 –1994, Exp. No. XX, 12 pp., Ecole Polytech., Palaiseau (1994)
Ivrii, V.: Asymptotics of the ground state energy of heavy molecules in the strong magnetic field. I. Russian J. Math. Phys. 4, no 1, 29–74 (1996)
Ivrii, V.: Heavy molecules in the strong magnetic field. Russian J. Math. Phys. 4, no 4, 449–456 (1996)
Ivrii, V.: Asymptotics of the ground state energy of heavy molecules in the strong magnetic field. II. Russian J. Math. Phys. 5, no 3, 321–354 (1997)
Ivrii, V.: Microlocal Analysis and Precise Spectral Asymptotics. Springer-Verlag (1998)
Ivrii, V., Sigal, I.M.: Asymptotics of the ground state energies of large Coulomb systems. Ann. Math. 138, 243 –335 (1993)
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Ivrii, V. (2009). Sharp Spectral Asymptotics for Dirac Energy. In: Isakov, V. (eds) Sobolev Spaces in Mathematics III. International Mathematical Series, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85652-0_4
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