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

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[B3] M. Birman. Discrete spectrum in the gaps of the perturbed periodic Schrödinger operator. II. Non-regular perturbations. St. Petersburg Math. J., 9 (1998), no. 6, pp. 1073-1095. | MR | Zbl

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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

[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

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