The limiting absorption principle is used to solve the scattering problem of time harmonic acoustic waves by penetrable objects in Sobolev spaces. The method is based on integral representation of the solution using t...The limiting absorption principle is used to solve the scattering problem of time harmonic acoustic waves by penetrable objects in Sobolev spaces. The method is based on integral representation of the solution using the Green＇s kernel of the Helmholtz equation.展开更多
We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions[30]and we prove that the principle of limiting absor...We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions[30]and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum.When an additional dissipative or smallness hypothesis is assumed on the potential,we show that the principle of limiting absorption holds at any point of the essential spectrum.展开更多
文摘The limiting absorption principle is used to solve the scattering problem of time harmonic acoustic waves by penetrable objects in Sobolev spaces. The method is based on integral representation of the solution using the Green＇s kernel of the Helmholtz equation.
文摘We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions[30]and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum.When an additional dissipative or smallness hypothesis is assumed on the potential,we show that the principle of limiting absorption holds at any point of the essential spectrum.
