Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPseudomodes for non-self-adjoint Dirac operators
138
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic non-semi-classical approach, which results in substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including superexponential ones.
rate research
Read More
Let $L$ be a non-negative self-adjoint operator acting on the space $L^2(X)$, where $X$ is a metric measure space. Let ${ L}=int_0^{infty} lambda dE_{ L}({lambda})$ be the spectral resolution of ${ L}$ and $S_R({ L})f=int_0^R dE_{ L}(lambda) f$ denote the spherical partial sums in terms of the resolution of ${ L}$. In this article we give a sufficient condition on $L$ such that $$ lim_{Rrightarrow infty} S_R({ L})f(x) =f(x), {rm a.e.} $$ for any $f$ such that ${rm log } (2+L) fin L^2(X)$. These results are applicable to large classes of operators including Dirichlet operators on smooth bounded domains, the Hermite operator and Schrodinger operators with inverse square potentials.
This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is self-adjoint on a usual Sobolev space whereas when the sector is non-convexit has a family of self-adjoint extensions parametrized by a complex number of theunit circle. As a byproduct of this analysis we are able to give self-adjointnessresults on polygones. We also discuss the question of distinguished self-adjointextensions and study basic spectral properties of the operator in the sector.
This note aims to give prominence to some new results on the absence and localization of eigenvalues for the Dirac and Klein-Gordon operators, starting from known resolvent estimates already established in the literature combined with the renowned Birman-Schwinger principle.
We study the trace class perturbations of the whole-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we refine the Lieb--Thirring inequality due to Hansmann--Katriel. The spectral enclosure for such operators is also discussed.
We prove the absence of eigenvaues of the three-dimensional Dirac operator with non-Hermitian potentials in unbounded regions of the complex plane under smallness conditions on the potentials in Lebesgue spaces. Our sufficient conditions are quantitative and easily checkable.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
