相关论文: Kato smoothing and Strichartz estimates for wave e…

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular…

We prove a microlocal smoothing effect of Schr\"odinger equations on manifolds. We employ radially homogeneous wavefront sets introduced by Ito and Nakamura (Amer. J. Math., 2009). In terms of radially homogeneous wavefront sets, we can…

We prove global-in-time Strichartz estimates for Schr\"odinger equations with multipole Aharonov--Bohm Hamiltonians on $\mathbb{R}^2$. As intermediate steps, we prove global-in-time local smoothing estimates for multipole Aharonov--Bohm…

Let $ H_0=-\dd+V_0 $ be a multidimensional Schr\"odinger ope\-rator with a real-valued potential and infinite band spectrum, and $H=H_0+V$ be its non-selfadjoint perturbation defined with the help of Kato approach. We prove Lieb--Thirring…

We introduce a general class of long-range magnetic potentials and derive high velocity limits for the scattering operators in quantum mechanics, in the case of two dimensions. We analyze the high velocity limits in the presence of an…

We construct time-dependent wave operators for Schr\"{o}dinger equations with long-range potentials on a manifold $M$ with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space…

This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown…

In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$…

We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schr\"odinger operator, in a quasi-convex domain~$\Omega$ with compact boundary, and magnetic potentials with components in…

The O(4) supersymmetry of the hydrogen atom is utilized to construct a complete basis using only the bound state wave functions. For a large class of perturbations, an expansion of the electron (exciton) wave function into such a complete…

This paper is concerned with the square root problem of Kato for the "sum" of linear operators in a Hilbert space ${\mathbb H}$. Under suitable assumptions, we show that if $A$ and $B$ are respectively m-scetroial linear operators…

We consider a non-self-adjoint $H$ given as the perturbation of a self-adjoint operator $H_0$. We suppose that $H$ is of the form $H=H_0+CWC$ where $C$ is a bounded, positive definite and relatively compact with respect to $H_0$, and $W$ is…

We obtain quasimode, eigenfunction and spectral projection bounds for Schr\"odinger operators, $H_V=-\Delta_g+V(x)$, on compact Riemannian manifolds $(M,g)$ of dimension $n\ge2$, which extend the results of the third author~\cite{sogge88}…

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

The Kondo lattice model of spin-1/2 local moments coupled to the conduction electrons at half-filling is studied for its orbital response to magnetic field on bipartite lattices. Through an effective charge dynamics, in a canonical…

We analyze spin-0 relativistic scattering of charged particles propagating in the exterior, $\Lambda \subset \mathbb{R}^3$, of a compact obstacle $K \subset \mathbb{R}^3$. The connected components of the obstacle are handlebodies. The…

We consider the following half wave Schr{\"o}dinger equation,$$\left(i \partial_{t}+\partial_{x }^2-\left|D_{y}\right|\right) U=|U|^{2} U$$on the plane $\mathbb{R}_x \times \mathbb{R}_y$. We prove the existence of modified wave operators…

In this paper we present and test a full discretization of all elements of the Calder\'on Calculus (layer potentials and integral operators) for the Helmholtz equation in smooth closed curves in the plane. The resulting integral equations…

In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schrodinger operator of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane.…

Existence of local-in-time unique solution and loss of smoothness of full Magnet-Hydro-Dynamics system (MHD) is considered for periodic initial data. The result is proven using Fujita-Kato's method in $\ell^1$ based (for the Fourier…