Related papers: Semiclassical analysis of a nonlinear eigenvalue p…
For the hypoelliptic differential operators $P={\partial^2_ x}+(x^k\partial_ y -x^l{\partial_t})^2$ introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of $k$ and $l$ left open in the analysis, the operators $P$ also…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
We aim at understanding how the non-commutation phenomena between a linear transport operator and a fractional diffusion allow the transport operator to satisfy hypoelliptic estimates on the whole space. Such hypoelliptic estimates are…
We study some accurate semiclassical resolvent estimates for operators that are neither selfadjoint nor elliptic, and applications to the Cauchy problem. In particular we get a precise description of the spectrum near the imaginary axis and…
We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth…
Aharonov-Albert-Vaidman's weak values are investigated by a semiclassical method. Examples of the semiclassical calculation that reproduces "anomalous" weak values are shown. Furthermore, a complex extension of Ehrenfest's quantum-classical…
We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
In this work, we review and extend some well known results for the eigenvalues of the Dirichlet $p-$Laplace operator to a more general class of monotone quasilinear elliptic operators. As an application we obtain some homogenization results…
We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity…
We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…
The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as perturbations of selfadjoint linear operators. Two methods are…
We present a finite difference method to compute the principal eigenvalue and the corresponding eigenfunction for a large class of second order elliptic operators including notably linear operators in nondivergence form and fully nonlinear…
We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions…
In this paper, we define and study semi-classical analysis and semi-classical limits on compact nil-manifolds. As an application, we obtain properties of quantum limits for sub-Laplacians in this context, and more generally for positive…
We investigate a technique to transform a linear two-parameter eigenvalue problem, into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by…
The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…
We consider the semi-classical limit of nonlinear Schrodinger equations in the presence of both a polynomial nonlinearity and thederivative in space of a polynomial nonlinearity. By working in a class of analytic initial data, we do not…