A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·, ·] given by [x,y] = 〈Jx,y〉 , x,y ∈ Cn. Characterizations of the J -chaotic order Log(A) J Log(B) are presented for J -selfadjoint matrices A,B with positive eigenvalues, in terms of operator functions involving the α -power mean and the J -relative entropy. An indefinite complete form of the Furuta inequality and s...

This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength ǫ of the perturbation is ≫ h (or sometimes only ≫ h2) and bounded from above by hδ for some δ > 0. We get a complete asymptotic descri...

Hill’s method is a means to numerically approximate spectra of linear differential operators with periodic coefficients. In this paper, we address different issues related to the convergence of Hill’s method. We show the method does not produce any spurious approximations, and that for selfadjoint operators, the method converges in a restricted sense. Furthermore, assuming convergence of an eig...

Voiculescu’s asymptotic freeness result for random matrices is improved to the sense of almost everywhere convergence. The asymptotic freeness almost everywhere is first shown for standard unitary matrices based on the computation of multiple moments of their entries, and then it is shown for rather general unitarily invariant selfadjoint random matrices (in particular, standard selfadjoint Gau...

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.

Let A be a Banach "-algebra. A is locally ¿"-equivalent if, for every selfadjoint element t e A, the closed *-subalgebra of A generated by / is *-isomorphic to a ¿"-algebra. In this paper it is shown that when A is locally ¿"-equivalent, and in addition every selfadjoint element in A has at most countable spectrum, then A is *-isomorphic to a ¿"-algebra.

Domain decomposition methods for the solution of semi-linear selfadjoint and non-selfadjoint singularly perturbed di erential equations are considered. An iterative domain decomposition algorithm suitable for parallelization is described and convergence of the algorithm is established. The implementation on a shared memory multiprocessor is described and numerical examples are presented to demo...

In this paper, a type of full multigrid method is proposed to solve non-selfadjoint Steklov eigenvalue problems. Multigrid iterations for corresponding selfadjoint and positive definite boundary value problems generate proper iterate solutions that are subsequently added the coarsest finite element space in order improve approximate eigenpairs on current mesh. Based multigrid, we propose new ad...