The main result of this paper is a generalization and sharpening of the Aubin-Dubinskii lemma concerning compact subsets in vectorvalued Lebesque spaces. In addition, there are given some newâ€¦ (More)

The pencil TÌƒ (Î», Îµ) = ÎµÎ»2I + Î»C + K, a singular perturbation of the linear pencil TÌƒ (Î», 0) = Î»C + K, is considered, and the asymptotic behavior of its large eigenvalues (i.e., those converging toâ€¦ (More)

Let A and B be selfadjoint operators on a Hilbert space H. We define the minimal index Î½(A, B) = min{#negative eigenvalues of Aâˆ’Î»B}, we connect it with various ideas in the literature and we connectâ€¦ (More)

where L is a symmetric elliptic operator and r is a locally integrable function on Rn. If r is of constant sign then this problem leads to a selfadjoint problem in the Hilbert space L2(|r|). In thisâ€¦ (More)

Consider the weighted eigenvalue problem Lu = (sgn x)u; (1) on the whole real line R where L = p(D) is a positive symmetric diierential operator with constant coeecients. This problem is a modelâ€¦ (More)

Krein space operator-theoretic methods are used to prove that the operator (sgnx)-j-j is similar to a selfadjoint operator in the Hubert space Â¿2(R) â€¢ Let L be a symmetric ordinary differentialâ€¦ (More)

We introduce the class N âˆž of all complex functions Q such that Q+(z) := z Â· Q(z) is a Nevanlinna function. If 0 âˆˆ D(Q) and limyâ†’âˆž Q(iy) = 0 we prove an integral representation Q(z) := âˆžâˆ« âˆ’âˆž dÏƒ(t)â€¦ (More)

Krein space operator-theoretic methods are used to prove that the operator (sgn x) d is similar to a selfadjoint operator in the Hilbert space L2 (R) . Let L be a symmetric ordinary differentialâ€¦ (More)

The handwritten medical record has been the method of choice for documenting health care data since the last millennium. Given this successful tenure, it would be natural to greet any new informationâ€¦ (More)

Certain continuity properties of the factors in generalized polar decompositions of real and complex matrices are studied. A complete characterization is given of those generalized polarâ€¦ (More)