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Discrete spectrum of zero order pseudodifferential operators

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the rate of convergence of eigenvalues to the endpoints of essential spectrum for zero order pseudodifferential operators on a compact manifold.
Rocznik
Strony
247--268
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
  • Chalmers University of Technology, Sweden
Bibliografia
  • [1] M.R. Adams, Spectral properties of zeroth-order pseudodifferential operators, J. Functional Analysis 52 (1983), no. 3, 420–441.
  • [2] M. Agranovich, B. Amosov, M. Levitin, Spectral problems for the Lamé system with spectral parameter in boundary conditions on smooth or nonsmooth boundary, Russ. J. Math. Phys. 6 (1999), no. 3, 247–281.
  • [3] K. Ando, H. Kang, Y. Miyanishi, Elastic Neumann–Poincaré operators in three dimensional smooth domains: polynomial compactness and spectral structure, Int. Math. Res. Not. IMRN 2019, no. 12, 3883–3900.
  • [4] K. Ando, H. Kang, Y. Miyanishi, Convergence rate for eigenvalues of the elastic Neumann–Poincaré operator in two dimensions, J. Math. Pures Appl. 140 (2020), 211–229.
  • [5] J. Barbe, Asymptotics of eigenvalues for hypoelliptic Hamiltonians without homogeneity assumptions, Math. Nachr. 224 (2001), 17–48.
  • [6] M. Birman, M. Solomyak, Asymptotic behavior of the spectrum of pseudodifferential operators with anisotropically homogeneous symbols, Vestnik Leningrad. Univ. 1977, no. 13, Mat. Meh. Astronom. vyp. 3, 13–21 [in Russian]; English translation in: Vestnik Leningr. Univ. Math. 10 (1982), 237–247.
  • [7] M. Birman, M. Solomyak, Estimates for the singular numbers of integral operators, Uspehi Mat. Nauk 32 (1977), no. 1 (193), 17–84 [in Russian]; English translation in: Russ. Math. Surveys 32 (1977), 15–89.
  • [8] F.H. Brownell, C.W. Clark, Asymptotic distribution of eigenvalues of the lower part of the Schrödinger operator spectrum, J. of Math. Mech. 10 (1961), 31–70.
  • [9] M. Capoferri, Diagonalization of elliptic systems via pseudodifferential projections, J. Differential Equations 313 (2022), 157–187.
  • [10] M. Capoferri, D. Vassiliev, Invariant subspaces of elliptic systems I: pseudodifferential projections, J. Funct. Anal. 282 (2022), no. 8, Paper no. 109402, 43 pp.
  • [11] M. Capoferri, G. Rozenblum, N. Saveliev, D. Vassiliev, Topological obstructions to the diagonalization of elliptic systems, Proc. Amer. Math. Soc. Ser. B 9 (2022), 472–486.
  • [12] Y. Colin de Verdière, Spectral theory of pseudodifferential operators of degree 0 and an application to forced linear waves, Anal. PDE 13 (2020), no. 5, 1521–1537.
  • [13] Y. Colin de Verdière, L. Saint-Raymont, Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0, Comm. Pure Appl. Math. 73 (2020), no. 2, 421–462.
  • [14] S. Dyatlov, M. Zworski, Microlocal analysis of forced waves, Pure Appl. Anal. 1 (2019), no. 3, 359–384.
  • [15] J. Galkowski, M. Zworski, Viscosity limits for 0th order pseudodifferential operators, Comm. Pure Appl. Math. 75 (2022), no. 8, 1798–1869.
  • [16] L. Hörmander, Analysis of Partial Differential Operators, vol. 3, Springer, 1985.
  • [17] V. Ivrii, Microlocal Analysis and Precise Spectral Asymptotics, Springer–Verlag, 1998.
  • [18] V. Ivrii, Microlocal Analysis, Sharp Spectral Asymptotics and Applications. II. Functional Methods and Eigenvalue Asymptotics, Springer, Cham, 2019.
  • [19] S. Levendorsky, The method of approximate spectral projection, Mathematics of the USSR-Izvestiya 27 (1986), no. 3, 451–502.
  • [20] S. Levendorsky, Asymptotic Distribution of Eigenvalues of Differential Operators, Kluwer, 1990.
  • [21] Y. Miyanishi, G. Rozenblum, Spectral properties of the Neumann-Poincarè operator in 3D elasticity, Int. Math. Res. Not. IMRN 2021, no. 11, 8715–8740.
  • [22] R. Ponge, Connes’ integration and Weyl’s laws, arXiv:2107.01242.
  • [23] G. Rozenblum, An asymptotics of the negative discrete spectrum of the Schrödinger operator, Mathematical Notes of the Academy of Sciences of the USSR 21 (1977), no. 3, 222–227.
  • [24] G. Rozenblum, Eigenvalue asymptotics for polynomially compact pseudodifferential operators, Algebra i Analiz 33 (2021), no. 2, 215–232.
  • [25] G. Rozenblum, On eigenvalues of the Neumann-Poincarè operator in 3D elasticity, J. Pseudo-Differ. Oper. Appl., to appear.
  • [26] M. Shubin, Pseudodifferential Operators and Spectral Theory, 2nd ed., Springer-Verlag, Berlin, 2001.
  • [27] Z. Tao, 0-th order pseudo-differential operators on the circle, arXiv:1909.06316.
  • [28] H. Tamura, The asymptotic distribution of discrete eigenvalues for Schrödinger operators, J. Math. Soc. Japan 29 (1977), no. 2, 189–218.
  • [29] H. Tamura, Asymptotic formulas with sharp remainder estimates for bound states of Schrödinger operators. I, J. Analyse Math. 40 (1981), 166–182.
  • [30] H. Tamura, Asymptotic formulas with sharp remainder estimates for bound states of Schrödinger operators. II, J. Analyse Math. 41 (1982), 85–108.
  • [31] J. Wang, The scattering matrix for 0th order pseudodifferential operators, arXiv:1909.06484.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fbe083c0-d7c9-4c41-bbd4-a965b1129777
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