Related papers: Non-Linear Eigenvalues and Analytic Hypoellipticit…

We give a semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity and obtain a general family of hypoelliptic, but not analytic hypoelliptic operators.

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…

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…

Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non…

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are…

For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…

Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract…

In this article, we determine the spectrum of real-analytic, non self-adjoint Toeplitz operators on compact K{\"a}hler manifolds and on the complex plane, on neighbourhoods of critical values of the symbol. We consider specifically critical…

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on…

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 use a classical result of Hildebrandt to establish simple conditions for the absence of eigenvalues of non-selfadjoint discrete and continuous Schr\"odinger operators on the boundary of their numerical range.

We find conditions on the potential of the non-self-adjoint Mathieu-Hill operator such that the all eigenvalues of the periodic, antiperiodic, Dirichlet and Neumann boundary value problems are simple.

We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…

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…

For relatively form-compact perturbations of non-negative selfadjoint operators, we obtain an upper bound on the number of discrete eigenvalues in half-planes separated from the positive real axis. The bound is given in terms of a partial…

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 fnd the asymptotics of eigenvalues of polynomially compact zero order pseudodiferential operators, the motivating example being the Neumann- Poincare operator in linear elasticity.

We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, {we give conditions under which these…