Gap and perturbation of non-semi-Fredholm operators.
Generalisation of Rellich's Theorem on Perturbation of (Essentially) Selfadjoin Operators.
Generalized Eigenvector Expansion for Weakly Perturbated Discrete Operators
Generalized quadratic operators and perturbations
We provide a complete description of the perturbation class and the commuting perturbation class of all generalized quadratic bounded operators with respect to a given idempotent bounded operator in the context of complex Banach spaces. Furthermore, we give simple characterizations of the generalized quadraticity of linear combinations of two generalized quadratic bounded operators with respect to a given idempotent bounded operator.
Generalized resolvents and spectrum for a certain class of perturbed symmetric operators.
Global minimizer of the ground state for two phase conductors in low contrast regime
The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap ε between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to ε and to small geometric perturbations of the optimal shape, that the global minimum of the first eigenvalue...