Related papers: Sharp Weyl laws with singular potentials
We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condition. In particular, the admissible class includes both…
We consider an open manifold which is the interior of a compact manifold with boundary. Assuming gauge invariance, we classify magnetic fields with compact support into being trapping or non-trapping. We study spectral properties of the…
Schroedinger operator on the half-line with periodic background potential perturbed by a certain potential of Wigner-von Neumann type is considered. The asymptotics of generalized eigenvectors for the values of the spectral parameter from…
We show that the global unique continuation principle holds for the parabolic fractional $p-$Laplace equation with very rough potentials $V(x,t) \in L^{p'}_tW^{-s,p'}_x$. Whereas the result is new even for the fractional $p-$Laplace…
The authors Matsaev and Mogulskii singled out a wide class of weak perturbation of a positive compact operator $H$, of the form $H(I+S)$, where $S$ is such a compact operator that $I+S$ is continuously invertible, which does not have a…
A Borg-Marchenko type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve inverse problem is used for this purpose. The asymptotic condition on the Weyl…
In this work, corrections for the Weyl law and Weyl conjecture in d dimensions are obtained and effects related to the polarization and area term are analyzed. The derived formalism is applied on the quasithermodynamics of the…
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…
We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we…
This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold $(M,g,\partial M)$ under the singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions…
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials $\mathbf V$ of Coulomb type: we characterise its…
Iosevich and Wyman have proved in ~\cite{IoWy} that the remainder term in classical Weyl law can be improved from $O(\lambda^{d-1})$ to $o(\lambda^{d-1})$ in the case of product manifold by using a famous result of Duistermaat and…
In this paper we consider the Sturm-Liuoville operator in the Hilbert space $L_2$ with the singular complex potential of $W^{-1}_2$ and two-point boundary conditions. For this operator we give sufficient conditions for norm resolvent…
We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law and a bound on its eta invariant. In the absence of a…
We prove a local unique continuation result for Schr\''odinger operators with time independent Lipschitz metrics and lower order terms which are Gevrey 2 in time and bounded in space. This implies global unique continuation from any open…
Weyl fermions are hypothetical chiral particles that can also manifest as excitations near three-dimensional band crossing points in lattice systems. These quasiparticles are subject to the Nielsen-Ninomiya "no-go" theorem when placed on a…
We study a class of PT-symmetric semiclassical Schr\"odinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the…
We prove that uniqueness for the Calder\'on problem on a Riemannian manifold with boundary follows from a hypothetical unique continuation property for the elliptic operator $\Delta+V+(\Lambda^{1}_{t}-q)\otimes (\Lambda^{2}_{t}-q)$ defined…
We study the self adjoint extensions of a class of non maximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank one perturbations (in the sense of \cite{AK}) of the Laplace…
We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features…