Some topics in spectral geometry
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). We consider all three cases.
Spectral analysis in a thin domain with periodically oscillating characteristics
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). ...
Spectral analysis of long wavelength periodic waves and applications.
Spectral analysis of non-compact manifolds using commutator methods
Spectral analysis of non-self-adjoint elliptic operators
Spectral analysis of strongly propagative systems.
Spectral Analysis of the Laplacian in Distorted Periodic Waveguides.
Spectral Analysis of the Laplacian in Domains with Cylinders.
Spectral analysis of variational inequalities
Spectral analysis of variational inequalities [Abstract of thesis]
Spectral and related properties about the Emden-Fowler equation -...u = ...e... on circular domains.
Spectral and scattering theory for symbolic potentials of order zero
Spectral and scattering theory for the Schrödinger operator with strongly oscillating potentials
Spectral and scattering theory in deformed optical wave guides.
Spectral approximation of variationally formulated eigenvalue problems on curved domains.
Spectral asymptotics and bifurcation for nonlinear multiparameter elliptic eigenvalue problems.
Spectral asymptotics for Hill's equation near the potential maximum
Spectral asymptotics for manifolds with cylindrical ends
The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to , where is the dimension of the manifold.
Spectral asymptotics for multi-quasi-elliptic operators in