Spectral asymptotics for Schrödinger operators with a degenerate potential
Spectral Asymptotics for the -Neumann Problem
Spectral asymptotics of Laplace operators on surfaces with cusps.
Spectral convergence of the discrete Laplacian on models of a metrized graph.
Spectral decomposition of Green’s integrals and existence of -solutions of matrix factorizations of the Laplace operator in a ball
Spectral Estimates for Magnetic Operators.
Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds.
Spectral estimates of vibration frequencies of anisotropic beams
The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics.
Spectral geometry and scattering theory for certain complete surfaces of finite volume.
Spectral Geometry and the Kaehler Condition for Complex Manifolds.
Spectral invariants for coupled spin-oscillators
This text deals with inverse spectral theory in a semiclassical setting. Given a quantum system, the haunting question is “What interesting quantities can be discovered on the spectrum that can help to characterize the system ?” The general framework will be semiclassical analysis, and the issue is to recover the classical dynamics from the quantum spectrum. The coupling of a spin and an oscillator is a fundamental example in physics where some nontrivial explicit calculations can be done.
Spectral limits for hyperbolic surfaces, I.
Spectral limits for hyperbolic surfaces, II.
Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...
Spectral projections for the twisted Laplacian
Let n ≥ 1, d = 2n, and let (x,y) ∈ ℝⁿ × ℝⁿ be a generic point in ℝ²ⁿ. The twisted Laplacian has the spectrum n + 2k = λ²: k a nonnegative integer. Let be the spectral projection onto the (infinite-dimensional) eigenspace. We find the optimal exponent ϱ(p) in the estimate for all p ∈ [2,∞], improving previous partial results by Ratnakumar, Rawat and Thangavelu, and by Stempak and Zienkiewicz. The expression for ϱ(p) is ϱ(p) = 1/p -1/2 if 2 ≤ p ≤ 2(d+1)/(d-1), ϱ(p) = (d-2)/2 - d/p if 2(d+1)/(d-1)...
Spectral properties of a solution to the Gellerstedt problem for mixed-type equations and their applications.
Spectral properties of compressible stratified flows.
Spectral properties of even order derivative operators.
Spectral properties of high contrast band-gap materials and operators on graphs.
Spectral properties of non-local uniformly-elliptic operators.