Absolute continuity of the spectrum of periodic operators of mathematical physics

Journées équations aux dérivées partielles (2000), article no. 18, 13 p.

@incollection{JEDP_2000____A18_0, author = {Tatiana Suslina}, title = {Absolute continuity of the spectrum of periodic operators of mathematical physics}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {18}, pages = {1--13}, publisher = {Universit\'e de Nantes}, year = {2000}, language = {en}, url = {https://proceedings.centre-mersenne.org/item/JEDP_2000____A18_0/} }

TY - JOUR AU - Tatiana Suslina TI - Absolute continuity of the spectrum of periodic operators of mathematical physics JO - Journées équations aux dérivées partielles PY - 2000 SP - 1 EP - 13 PB - Université de Nantes UR - https://proceedings.centre-mersenne.org/item/JEDP_2000____A18_0/ LA - en ID - JEDP_2000____A18_0 ER -

%0 Journal Article %A Tatiana Suslina %T Absolute continuity of the spectrum of periodic operators of mathematical physics %J Journées équations aux dérivées partielles %D 2000 %P 1-13 %I Université de Nantes %U https://proceedings.centre-mersenne.org/item/JEDP_2000____A18_0/ %G en %F JEDP_2000____A18_0

Tatiana Suslina. Absolute continuity of the spectrum of periodic operators of mathematical physics. Journées équations aux dérivées partielles (2000), article no. 18, 13 p. https://proceedings.centre-mersenne.org/item/JEDP_2000____A18_0/

[BSu1] M. Sh. Birman and T. A. Suslina, Two-dimensional periodic magnetic Hamiltonian is absolutely continuous, Algebra i Analiz 9 (1997), no. 1, 32-48. English transl. St. Petersburg Math. J. 9 (1998), no. 1. | Zbl

[BSu2] M. Sh. Birman and T. A. Suslina, Absolute continuity of the two-dimensional periodic magnetic Hamiltonian with discontinuous vector-valued potential, Algebra i Analiz 10 (1998), no. 4, 1-36. English transl. St. Petersburg Math. J. 10 (1999), no. 4. | Zbl

[BSu3] M. Sh. Birman and T. A. Suslina, The periodic Dirac operator is absolutely continuous, Integral Equations and Operator Theory 34 (1999), no. 4, 377-395. | MR | Zbl

[BSu4] M. Sh. Birman and T. A. Suslina, Periodic magnetic Hamiltonian with variable metric. The problem of absolute continuity, Algebra i Analiz 11 (1999), no. 2, 1-40. English transl. St. Petersburg Math. J. 11 (2000), no. 2. | Zbl

[BSu5] M. Sh. Birman and T. A. Suslina, On the absolute continuity of the periodic Schrödinger and Dirac operators with magnetic potential, Diff. Eq. Math. Physics, Proc. of an Intern. Conf. held at the University of Alabama at Birmingham, March 16-20, 1999, 17-25.

[BSuSht] M. Sh. Birman, T. A. Suslina and R. G. Shterenberg, Absolute continuity of the spectrum of the Schrödinger operator with delta-like potential supported by a periodic graph, in preparation.

[D1] L. Danilov, On the spectrum of the Dirac operator with periodic potential in ℝn, Teor. Mat. Fiz. 85 (1990), no. 1, 41-53. | MR | Zbl

[D2] L. Danilov, Resolvent estimates and the spectrum of the Dirac operator with periodic potential, Teor. Mat. Fiz. 103 (1995), no. 1, 3-22. | MR | Zbl

[D3] L. Danilov, On the spectrum of the twodimensional periodic Dirac operator, Teor. Mat. Fiz. 118 (1999), no. 1, 3-14. | MR | Zbl

[D4] L. Danilov, Private communication (1999).

[HemHer] R. Hempel and I. Herbst, Bands and gaps for periodic magnetic Hamiltonians, Oper. Theory Adv. Appl., 78 (1995), 175-184. | MR | Zbl

[K1] P. Kuchment, Floquet theory for partial differential equations, Birkhäuser, Basel, 1993. | MR | Zbl

[K2] P. Kuchment, Private communication (2000).

[K3] P. Kuchment, The mathematics of photonic crystals, To appear in «Math. Modeling in Optical Science», SIAM. | Zbl

[KL] P. Kuchment and S. Levendorskii, On the absolute continuity of spectra of periodic elliptic operators, Oper. Theory Adv. Appl. 108 (1999), 291-297. | MR | Zbl

[M1] A. Morame, Absence of singular spectrum for a perturbation of a two-dimensional Laplace-Beltrami operator with periodic electro-magnetic potential, J. Phys. A: Math. Gen. 31 (1998), 7593-7601. | MR | Zbl

[M2] A. Morame, The absolute continuity of the spectrum of Maxwell operator in a periodic media, Preprint 99-308 in mp-arc (1999).

[RSi] M. Reed and B. Simon, Methods of modern mathematical physics, IV, Academic Press, New York, 1975. | Zbl

[Sh1] Z. Shen, On absolute continuity of the periodic Schrödinger operators, Preprint ESI 597, Vienna (1998).

[Sh2] Z. Shen, On absolute continuity of the periodic Schrödinger operators, Preprint 99-189 in mp-arc (1999).

[Sh3] Z. Shen, The periodic Schrödinger operator with potentials in the C. Fefferman-Phong class, Preprint 99-455 in mp-arc (1999).

[So1] A. Sobolev, Absolute continuity of the periodic magnetic Schrödinger operator, Invent. Math. 137 (1997), 85-112. | MR | Zbl

[So2] A. Sobolev, Private communication (1998).

[T] L. Thomas, Time dependent approach to scattering from impurities in a crystal, Comm. Math. Phys. 33 (1973), 335-343. | MR