Related papers: Semi-classical dispersive estimates

We study the distribution of eigenvalues for non-selfadjoint perturbations of selfadjoint semiclassical analytic pseudodifferential operators in dimension two, assuming that the classical flow of the unperturbed part is completely…

In this paper we explore a certain class of non-selfadjoint operators acting in a complex separable Hilbert space. We consider a perturbation of a non-selfadjoint operator by an operator that is also non-selfadjoint. Our consideration is…

We prove optimal high-frequency resolvent estimates for perturbations by large magnetic and electric potentials

This is the second in a series of works devoted to small non-selfadjoint perturbations of selfadjoint semiclassical pseudodifferential operators in dimension 2. As in our previous work, we consider the case when the classical flow of the…

We study a class of quasi-linear parabolic equations defined on a separable Hilbert space, depending on a small parameter in front of the second order term. Through the nonlinear semigroup associated with such equation, we introduce the…

The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.

We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…

In this paper, we study one-dimensional linear Schr\"odinger equations with multiple moving potentials, known as transfer charge models. Focusing on the non-self-adjoint setting that arises in the study of solitons, we systematically…

We prove a family of dispersive estimates for the higher order Schr\"odinger equation $iu_t=(-\Delta)^mu +Vu$ for $m\in \mathbb N$ with $m>1$ and $2m<n<4m$. Here $V$ is a real-valued potential belonging to the closure of $C_0$ functions…

We prove dispersive and Strichartz estimates for Schr\"{o}dinger equations on normal real form symmetric spaces. These estimates apply to the well-posedness and scattering for the nonlinear Schr\"{o}dinger equations.

In this paper, we study the linear and nonlinear Schr\"odinger equations with a time-decaying harmonic oscillator and inverse-square potential. This model retains a form of scale invariance, and using this property, we demonstrate the…

We prove $L^{p}$ and weighted $L^{p}$ estimates for bounded functions of a selfadjoint operator satisfying both a pointwise gaussian estimate for its heat kernel and a finite speed of propagation property. As an application, we obtain…

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator $L$, without assuming the gradient estimate for its spectral kernel. The result applies to the cases…

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schr\"{o}dinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the…

We extend previous semi-classical resolvent estimates for real-valued compactly supported $L^\infty$ potentials to non-compactly supported $L^\infty$ potentials.

This is the third paper in a series analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We analyze the distribution of phase shifts, or equivalently, eigenvalues of the scattering matrix, $S_h(E)$, for…

In this paper we consider linear, time dependent Schr\"odinger equations of the form ${\rm i} \partial_t \psi = K_0 \psi + V(t) \psi$, where $K_0$ is a strictly positive selfadjoint operator with discrete spectrum and constant spectral…

We consider semiclassically scaled Schrodinger equations with an external potential and a highly oscillatory periodic potential. We construct asymptotic solutions in the form of semiclassical wave packets. These solutions are concentrated…

In this work we study traces of spectral decompositions corresponding to self adjoint elliptic pseudo-differential operators of distributions in the classes of Soboloev-Liouville and Nikolskii-Besov

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…