Về các Lacuna trong Quang phổ của Toán tử Laplace với Điều kiện Biên Dirichlet trong một Dải có Biên Dao động

G. Barbatis and L. Parnovski, “Bethe–Sommerfeld conjecture for pseudo-differential perturbation,” Commun. Part. Differ. Equ., 34, No. 4, 383–418 (2009). C. B. E. Beeken, Periodic Schrödinger operators in dimension two: constant magnetic fields and boundary-value problems, Ph.D. thesis., Univ. of Sussex, Brighton (2002). D. I. Borisov, “On lacunas in the lower part of the spectrum of a periodic magnetic operator in a band,” Sovr. Mat. Fundam. Napravl., 63, No. 3, 373–391 (2017). D. I. Borisov, “On lacunas in the spectrum of the Laplacian in a band perturbed by a bounded periodic operator,” Ufim. Mat. Zh., 10, No. 2, 13–29 (2018). D. I. Borisov, “The absence of lacunas in the lower part of the spectrum of the Laplacian with frequent alternation of boundary conditions in a band,” Teor. Mat. Fiz., 195, No. 2, 225–239 (2018). D. Borisov, R. Bunoiu, and G. Cardone, “On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition,” Ann. Inst. H. Poincaré, 11, No. 8, 1591–1627 (2010). D. Borisov, R. Bunoiu, and G. Cardone, “On a waveguide with an infinite number of small windows,” Comp. Rend. Math., 349, No. 1-2, 53–56 (2011). D. Borisov, R. Bunoiu, and G. Cardone, “Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics,” Z. Angew. Math. Phys., 64, No. 3, 439–472 (2013). D. Borisov and G. Cardone, “Homogenization of the planar waveguide with frequently alternating boundary conditions,” J. Phys. A. Math. Gen., 42, No. 36, 365205 (2009). D. Borisov, G. Cardone, and T. Durante, “Homogenization and uniform resolvent convergence for elliptic operators in a strip perforated along a curve,” Proc. Roy. Soc. Edinburgh. Sec. A. Math., 146, No. 6, 1115–1158 (2016). D. Borisov, G. Cardone, L. Faella, and C. Perugia, “Uniform resolvent convergence for a strip with fast oscillating boundary,” J. Differ. Equ., 255, No. 12, 4378–4402 (2013). B. E. J. Dahlberg and E. Trubowitz, “A remark on two dimensional periodic potentials,” Comment. Math. Helvet., 57, No. 1, 130–134 (1982). B. Helffer and A. Mohamed, “Asymptotics of the density of states for the Schrödinger operator with periodic electric potential,” Duke Math. J., 92, No. 1, 1–60 (1998). Y. Karpeshina, “Spectral properties of the periodic magnetic Schrödinger operator in the highenergy region. Two-dimensional case,” Commun. Math. Phys., 251, No. 3, 473–514 (2004). A. Mohamed, “Asymptotic of the density of states for the Schr¨odinger operator with periodic electromagnetic potential,” J. Math. Phys., 38, No. 8, 4023–4051 (1997). L. Parnovski, “Bethe–Sommerfeld conjecture,” Ann. Inst. H. Poincaré., 9, No. 3, 457–508 (2008). L. Parnovski and A. Sobolev, “On the Bethe–Sommerfeld conjecture for the polyharmonic operator,” Duke Math. J., 107, No. 2, 209–238 (2001). L. Parnovski and A. Sobolev, “Bethe–Sommerfeld conjecture for periodic operators with strong perturbations,” Invent. Math., 181, No. 3, 467–540 (2010). M. M. Skriganov, “Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators,” Tr. Mat. Inst. V. A. Steklova, 171, 3–122 (1985). M. M. Skriganov and A. V. Sobolev, “Asymptotic estimates for spectral zones of peiodic Schrödinger operators,” Alg. Anal., 17, No. 1, 276–288 (2005). M. M. Skriganov and A. V. Sobolev, “Variation of the number of lattice points in large balls,” Acta Arithm., 120, No. 3, 245–267 (2005).