Geodesic
On the spectrum of polyharmonic operators with limit-periodic potentials
Algebra i analiz, Tome 17 (2005) no. 5, pp. 164-189.

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M. M. Skriganov; A. V. Sobolev. On the spectrum of polyharmonic operators with limit-periodic potentials. Algebra i analiz, Tome 17 (2005) no. 5, pp. 164-189. http://geodesic.mathdoc.fr/item/AA_2005_17_5_a5/

[1] Abramovits M., Stigan I. (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979 | MR

[2] Avron J., Simon B., “Almost periodic Schrödinger operators. I. Limit periodic potentials”, Comm. Math. Phys., 82 (1981), 101–120 | DOI | MR | Zbl

[3] Dahlberg B. E. J., Trubowitz E., “A remark on two-dimensional periodic potentials”, Comment. Math. Helv., 57 (1982), 130–134 | DOI | MR | Zbl

[4] Hare K. E., O'Neil T. C., “$N$-fold sums of Cantor sets”, Mathematika, 47 (2002):1–2 (2000), 243–250 | MR | Zbl

[5] Helffer B., Mohamed A., “Asymptotic of the density of states for the Schrödinger operator with periodic electric potential”, Duke Math. J., 92 (1998), 1–60 | DOI | MR | Zbl

[6] Karpeshina Yu., “On the density of states for the periodic Schrödinger operator”, Ark. Mat., 38 (2000), 111–137 | DOI | MR | Zbl

[7] Karpeshina Yu., Spectral properties of a polyharmonic operator with limit-periodic potential in two dimensions, talk at the Workshop on Spectral Theory of Schrödinger Operators (Montreal, July 2004)

[8] Konyagin S. V., Skriganov M. M., Sobolev A. V., “On a lattice point problem arising in the spectral analysis of periodic operators”, Mathematika, 50 (2003), 87–98, (2005) | MR | Zbl

[9] Mendes P., Oliveira F., “On the topological structure of the arithmetic sum of two Cantor sets”, Nonlinearity, 7 (1994), 329–343 | DOI | MR | Zbl

[10] Parnovski L., Sobolev A. V., “Lattice points, perturbation theory and the periodic polyharmonic operator”, Ann. H. Poincaré, 2 (2001), 573–581 | DOI | MR | Zbl

[11] Skriganov M. M., Geometricheskie i arifmeticheskie metody v spektralnoi teorii mnogomernykh periodicheskikh operatorov, Tr. Mat. in-ta AN SSSR, 171, 1985, 122 pp. | MR | Zbl

[12] Skriganov M., “The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential”, Invent. Math., 80 (1985), 107–121 | DOI | MR | Zbl

[13] Skriganov M. M., Sobolev A. V., “Asimptoticheskie otsenki dlya spektralnykh zon periodicheskikh operatorov Shrëdingera”, Algebra i analiz, 17:1 (2005), 276–288 | MR

[14] Shubin M. A., “Spektralnaya teoriya i indeks ellipticheskikh operatorov s pochti-periodicheskimi koeffitsientami”, Uspekhi mat. nauk, 34:2(206) (1979), 95–135 | MR | Zbl