Einschliessungsaussagen für Differentialoperatoren vierter Ordnung und ein Verfahren zur Berechnung von Schrankenfunktionen.
Essential descent spectrum and commuting compact perturbations.
Evolution semigroups for nonautonomous Cauchy problems.
Extremal perturbations of semi-Fredholm operators
Let T be a bounded operator on an infinite-dimensional Banach space X and Ω a compact subset of the semi-Fredholm domain of T. We construct a finite rank perturbation F such that min[dim N(T+F-λ), codim R(T+F-λ)] = 0 for all λ ∈ Ω, and which is extremal in the sense that F² = 0 and rank F = max{min[dim N(T-λ), codim R(T-λ)] : λ ∈ Ω.
Faces in the Unit Ball of the Dual of L (Rn).
Finite-rank perturbations of positive operators and isometries
We completely characterize the ranks of A - B and for operators A and B on a Hilbert space satisfying A ≥ B ≥ 0. Namely, let l and m be nonnegative integers or infinity. Then l = rank(A - B) and for some operators A and B with A ≥ B ≥ 0 on a Hilbert space of dimension n (1 ≤ n ≤ ∞) if and only if l = m = 0 or 0 < l ≤ m ≤ n. In particular, this answers in the negative the question posed by C. Benhida whether for positive operators A and B the finiteness of rank(A - B) implies that of . For...
Form perturbations of the second quantized Dirac field.
Fractional Laplacian with singular drift
For α ∈ (1,2) we consider the equation , where b is a time-independent, divergence-free singular vector field of the Morrey class . We show that if the Morrey norm is sufficiently small, then the fundamental solution is globally in time comparable with the density of the isotropic stable process.
Fredholm points of compactly pertubed bounded linear operators
Fredholm Toeplitz operators on strongly pseudoconvex domains
Functions of operators and their commutators in perturbation theory
This paper shows some directions of perturbation theory for Lipschitz functions of selfadjoint and normal operators, without giving precise proofs. Some of the ideas discussed are explained informally or for the finite-dimensional case. Several unsolved problems are mentioned.
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...
Holomorphe Störungstheorie in lokalkonvexen Räumen.
Holomorphic Operator Families and Stability of Selfadjointness.
Identification problems for degenerate parabolic equations
This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different...