Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.
Eigenfunctions of the laplacian, quantum chaos, and computation
Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations
In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds
Eigenvalue problems for a mixed-type equation with two singular coefficients.
Eigenvalue problems for the -Laplacian with indefinite weights.
Eigenvalue problems with indefinite weight
We consider the linear eigenvalue problem -Δu = λV(x)u, , and its nonlinear generalization , . The set Ω need not be bounded, in particular, is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues .
Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions
Elementary linear algebra for advanced spectral problems
We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical...
Elliptische Differentialgleichungen mit variablen Koeffizienten in Gebieten mit unbeschränktem Rand.
Entropy and localization of eigenfunctions
Équation de transport. Théorie spectrale et approximation de la diffusion
Équations des ondes amorties
Errata - De l'exposé n° XVII de B. Helffer et de J. Sjöstrand «Analyse semi-classique pour l'équation de Harper»
Erratum of “The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent”
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...
Essential Selfadjointness of Dirac Operators with a Strongly Singular Potential.
Essential self-adjointness of symmetric linear relations associated to first order systems
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert space. In this case even regularity is nontrivial. We will announce a regularity result and discuss criteria...
Estimates for the Asymptotic Behavior of Solutions of the Helmholtz Equation, with an Application to Second order Elliptic Differential Operators with Variable Coefficients.
Estimates for the asymptotic behavior of solutions of the Helmholtz equation, with an application to second order elliptic differential operators with variable coefficients (Erratum).
Estimates of the heat content on a class of domains.