Accurate Spectral Asymptotics for periodic operators
Journées équations aux dérivées partielles, (1999), article no. 5, 11 p.

Asymptotics with sharp remainder estimates are recovered for number 𝐍(τ) of eigenvalues of operator A(x,D)-tW(x,x) crossing level E as t runs from 0 to τ, τ. Here A is periodic matrix operator, matrix W is positive, periodic with respect to first copy of x and decaying as second copy of x goes to infinity, E either belongs to a spectral gap of A or is one its ends. These problems are first treated in papers of M. Sh. Birman, M. Sh. Birman-A. Laptev and M. Sh. Birman-T. Suslina.

@article{JEDP_1999____A5_0,
     author = {Ivrii, Victor},
     title = {Accurate Spectral Asymptotics for periodic operators},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Universit\'e de Nantes},
     year = {1999},
     zbl = {01810578},
     mrnumber = {2000h:35125},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1999____A5_0}
}
Ivrii, Victor. Accurate Spectral Asymptotics for periodic operators. Journées équations aux dérivées partielles,  (1999), article  no. 5, 11 p. http://www.numdam.org/item/JEDP_1999____A5_0/

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[B2] M. Birman. The discrete spectrum of the periodic Schrödinger operator perturbed by a decreasing potential. St. Petersburg Math. J., 8 (1997), no. 1, pp. 1-14. | MR 97h:47047 | Zbl 0866.35087

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[BLS] M. Birman, A. Laptev, T. Suslina. Discrete spectrum of the twodimensional periodic elliptic second order operator perturbed by a decreasing potential. I. Semiinfinite gap (in preparation). | Zbl 01637582

[BS] M. Birman, T. Suslina. Birman, Suslina. Discrete spectrum of the twodimensional periodic elliptic second order operator perturbed by a decreasing potential. II. Internal gaps (in preparation). | Zbl 01637582

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[Ivr2] V. Ivrii. Accurate Spectral Asymptotics for Neumann Laplacian in domains with cusps (to appear in Applicable Analysis).

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