Abstract:
A method is developed for proving a classical formula for the asymptotic behavior of the spectrum in various spectral problems, with a certain estimate of the remainder. Considered as applications are linear pencils both on bounded and on unbounded regions, problems in the theory of shells, and the problem of the asymptotic behavior of a discrete spectrum accumulating to the boundary of the essential spectrum for Schrödinger and Dirac operators.
Bibliography: 74 titles.
This publication is cited in the following 9 articles:
V. I. Bezyaev, “Ob asimptotike plotnosti sostoyanii gipoellipticheskikh pochti-periodicheskikh sistem”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 593–604
A. I. Karol', “Asymptotics of Spectra of Compact Pseudodifferential Operators with Nonsmooth Symbols with Respect to Spatial Variables”, J Math Sci, 226:4 (2017), 355
V. M. Kaplitskiǐ, “Asymptotics of the distribution of eigenvalues of a selfadjoint second order hyperbolic differential operator on the two-dimensional torus”, Siberian Math. J., 51:5 (2010), 830–846
K. Kh. Boimatov, “Asymptotics of spectral projectors of pseudodifferential operators”, Funct. Anal. Appl., 26:1 (1992), 42–44
A. S. Andreev, “Estimates of the spectrum of compact pseudodifferential operators in unbounded domains”, Math. USSR-Sb., 70:2 (1991), 431–443
S. Z. Levendorskii, “On types of degenerate elliptic operators”, Math. USSR-Sb., 66:2 (1990), 523–540
K. Kh. Boimatov, A. G. Kostyuchenko, “Eigenvalues of the equation Au=λBu on a compact manifold without boundary”, Funct. Anal. Appl., 23:1 (1989), 52–53
A. S. Andreev, “Asymptotics of the spectrum of compact pseudodifferential operators in a Euclidean domain”, Math. USSR-Sb., 65:1 (1990), 205–228
S. Z. Levendorskii, “Non-classical spectral asymptotics”, Russian Math. Surveys, 43:1 (1988), 149–192
Citation in format AMSBIB
Contact us: