Mersenne banner

Books, Proceedings and Seminars of Centre Mersenne

  • Books
  • Seminars
  • Proceedings
  • All
  • Author
  • Title
  • References
  • Keywords
  • Full text
NOT
Between and
  • All
  • Author
  • Title
  • Date
  • References
  • Keywords
  • Full text
  • Previous
  • Journées équations aux dérivées partielles
  • Year 1999
  • article no. 5
  • Next
Accurate Spectral Asymptotics for periodic operators
Victor Ivrii
Journées équations aux dérivées partielles (1999), article no. 5, 11 p.
  • Abstract

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 information
  • Export
  • How to cite
MR: 2000h:35125 | Zbl: 01810578
  • BibTeX
  • RIS
  • EndNote
@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/}
}
TY  - JOUR
AU  - Victor Ivrii
TI  - Accurate Spectral Asymptotics for periodic operators
JO  - Journées équations aux dérivées partielles
PY  - 1999
PB  - Université de Nantes
UR  - https://proceedings.centre-mersenne.org/item/JEDP_1999____A5_0/
LA  - en
ID  - JEDP_1999____A5_0
ER  - 
%0 Journal Article
%A Victor Ivrii
%T Accurate Spectral Asymptotics for periodic operators
%J Journées équations aux dérivées partielles
%D 1999
%I Université de Nantes
%U https://proceedings.centre-mersenne.org/item/JEDP_1999____A5_0/
%G en
%F JEDP_1999____A5_0
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/
  • References
  • Cited by

[B1] M. Birman. The discrete spectrum in gaps of the perturbed periodic Schrödinger operator. I. Regularperturbations. Boundary value problems, Schrödinger operators, deformation quantization, Math. Top., 8, Akademie Verlag, Berlin, 1995, pp. 334-352. | MR | Zbl

[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 | Zbl

[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

[BL1] M. Birman, A. Laptev. The negative discrete spectrum of a two-dimensional Schrödinger operator. Comm. Pure Appl. Math., 49 (1996), no. 9, pp. 967-997. | MR | Zbl

[BL2] M. Birman, A. Laptev. «Non-standard» spectral asymptotics for a two-dimensional Schrödinger operator. Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes, 12 (1997), pp. 9-16. | MR | Zbl

[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

[Ivr1] V. Ivrii. Microlocal Analysis and Precise Spectral Asymptotics. Springer-Verlag, SMM, 1998, 731+15 pp. | MR | Zbl

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

[JMS] V. Jakšić, S. Molčanov and B. Simon. Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps. J. Func. Anal., 106, (1992), pp. 59-79. | MR | Zbl

[Sol1] M. Solomyak. On the negative discrete spectrum of the operator -ΔN -αV for a class of unbounded domains in Rd, CRM Proceedings and Lecture Notes, Centre de Recherches Mathematiques, 12, (1997), pp. 283-296. | MR | Zbl

Web publisher : Published by : Developed by :
  • Follow us