Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides

DOI10.1070/IM8928zbMath1458.35031MaRDI QIDQ5147330

Sergueï A. Nazarov

Publication date: 3 February 2021

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

zbMATH Keywords

elliptic systemsDirichlet or Neumann boundary conditionsalmost standing wavesself-adjoint extensions of differential operatorsvirtual levelsthresholds of continuous spectrumspaces with separated asymptotic conditions

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Singular perturbations in context of PDEs (35B25) General topics in linear spectral theory for PDEs (35P05) (Semi-) Fredholm operators; index theories (47A53) Antennas, waveguides in optics and electromagnetic theory (78A50) Quantum waveguides, quantum wires (82D77)

Related Items (10)

Rayleigh waves for elliptic systems in domains with periodic boundaries ⋮ On perturbation of thresholds in essential spectrum under coexistence of virtual level and spectral singularity ⋮ Spectral gaps in a thin-walled infinite rectangular Dirichlet box with a periodic family of cross walls ⋮ Two-dimensional asymptotic models of thin cylindrical elastic gaskets ⋮ On the bifurcation of thresholds of the essential spectrum with a spectral singularity ⋮ Localization of eigenfunctions in the Dirichlet beaker ⋮ On the one-dimensional asymptotic models of thin Neumann lattices ⋮ Trapping of waves in semiinfinite Kirchhoff plate with periodically damaged edge ⋮ The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides ⋮ Propagating and standing Rayleigh waves near rivet chains connecting Kirchhoff plates

Cites Work

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• Discrete spectrum of cranked quantum and elastic waveguides
• Opening of a gap in the continuous spectrum of a periodically perturbed waveguide
• Localized elastic fields in periodic waveguides with defects
• Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide
• The Mandelstam energy radiation conditions and the Umov-Poynting vector in elastic waveguides
• Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide
• On computation of waveguide scattering matrices for the Maxwell system
• Eigenvalues of the Laplace operator with the Neumann conditions at regular perturbed walls of a waveguide
• Convergence of spectra of graph-like thin manifolds
• Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold
• Local perturbations of quantum waveguides
• Zero radius interaction for the biharmonic and polyharmonic equations
• Selfadjoint extensions of the Neumann Laplacian in domains with cylindrical outlets
• Non-self-adjoint elliptic problems with a polynomial property in domains possessing cylindrical outlets to infinity
• The eigenfrequencies of a slightly curved isotropic strip clamped between absolutely rigid profiles
• Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients
• On the eigenvalues of finitely perturbed Laplace operators in infinite cylindrical domains
• Nonunique continuation for the Maxwell system
• Near-threshold effects of the scattering of waves in a distorted elastic two-dimensional waveguide
• Quantum waveguides
• Scattering solutions in networks of thin fibers: small diameter asymptotics
• Various manifestations of wood anomalies in locally distorted quantum waveguides
• A criterion for the existence of decaying solutions in the problem on a resonator with a cylindrical waveguide
• Edge resonance in an elastic semi-infinite cylinder
• Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones
• Umov-Mandelshtam radiation conditions in elastic periodic waveguides
• Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues
• Spectra of graph neighborhoods and scattering
• Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder
• Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains
• The theory of extensions and explicitly-soluble models
• ELLIPTIC BOUNDARY VALUE PROBLEMS WITH PERIODIC COEFFICIENTS IN A CYLINDER
• [Russian Text Ignored.]
• Edge resonance in an elastic semi-strip
• Existence theorems for trapped modes
• The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
• Asymptotic analysis of an arbitrary anisotropic plate of variable thickness (sloping shell)
• SELFADJOINT EXTENSIONS OF THE DIRICHLET PROBLEM OPERATOR IN WEIGHTED FUNCTION SPACES
• ABSOLUTE CONTINUITY IN PERIODIC WAVEGUIDES
• Geometric coupling thresholds in a two-dimensional strip
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• Method for computing waveguide scattering matrices in the vicinity of thresholds
• The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap
• Elastic waves trapped by a homogeneous anisotropic semicylinder
• Discrete spectrum of an asymmetric pair of waveguides coupled through a window
• ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
• Floquet theory for partial differential equations
• Floquet theory for partial differential equations

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