Related papers: Spectral Properties of Hypoelliptic Operators

In this article, we will consider second order uniformly elliptic operators of divergence form defined on R^n with measurable coefficients. Mainly, we will give estimates on the dimension of space of solutions that grow at most polynomially…

The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of…

We consider a class of Hankel operators $H$ realized in the space $L^2 ({\Bbb R}_{+}) $ as integral operators with kernels $h(t+s)$ where $h(t)=P (\ln t) t ^{-1}$ and $P(X)= X^n+p_{n-1} X^{n-1}+\cdots$ is an arbitrary real polynomial of…

Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued…

We consider Kramers-Fokker-Planck operators with general degenerate coefficients. We prove semiclassical hypocoercivity estimates for a large class of such operators. Then, we manage to prove Eyring-Kramers formulas for the bottom of the…

Polyharmonic functions f of infinite order and type {\tau} on annular regions are systematically studied. The first main result states that the Fourier-Laplace coefficients f_{k,l}(r) of a polyharmonic function f of infinite order and type…

We consider the complex solvable non-commutative two dimensional Lie algebra $L$, $L=<y>\oplus <x>$, with Lie bracket $[x,y]=y$, as linear bounded operators acting on a complex Hilbert space $H$. Under the assumption $R(y)$ closed, we…

For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…

The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…

The wave operators $W_\pm(H_1,H_0)$ of two selfadjoint operators $H_0$ and $H_1$ are analyzed at asymptotic spectral values. Sufficient conditions for $\|(W_\pm(H_1,H_0)-P_{1}^\mathrm{ac}P_{0}^\mathrm{ac})f(H_0)\| <\infty$ are given, where…

We consider operators $-\Delta + X$ where $X$ is a constant vector field, in a bounded domain and show spectral instability when the domain is expanded by scaling. More generally, we consider semiclassical elliptic boundary value problems…

In this paper, it is shown that some new phenomenon related to the spectra of Toeplitz operators with bounded harmonic symbols on the Bergman space. On the one hand, we prove that the spectrum of the Toeplitz operator with symbol…

Let $\G$ be a Carnot group of homogeneous dimension $M$ and $\Delta$ its horizontal sublaplacian. For $\alpha\in(0,M)$ we show that operators of the form $H_\alpha:=(-\Delta)^\alpha+V$ have no singular spectrum, under generous assumptions…

This article deals with properties of spectra of operators on C(K)-spaces with the Grothendieck property (e.g. l^{\infty}) and application to so called J-class operators introduced by A. Manoussos and G. Costakis. We will show that C(K) has…

Hermite polynomials, which are associated to a Gaussian weight and solve the Laplace equation with a drift term of linear growth, are classical in analysis and well-understood via ODE techniques. Our main contribution is to give explicit…

We provide a precise description of the bottom of the spectrum in the semiclassical limit of a harmonic-type Schr\"odinger operator with an inverse square potential. By exploiting the connection between the eigenfunctions of these operators…

In this paper we study nonlocal equations driven by the fractional powers of hypoelliptic operators in the form $$\mathscr K u = \mathscr A u - \partial_t u \overset{def}{=} \operatorname{tr}(Q \nabla^2 u) + <BX,\nabla u> - \partial_t u,$$…

We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator $(-\Delta)^m$ with $ m \geq 2$. We show that the map from the coefficients to a certain bilinear form is injective. We…

The hyperoctahedral group is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators T_i, i=1,..,N (the dimension of the underlying Euclidean space). These operators are analogous to…

The study of spectral properties of natural geometric elliptic partial differential operators acting on smooth sections of vector bundles over Riemannian manifolds is a central theme in global analysis, differential geometry and…