Fonction spectrale d'opérateurs non elliptiques
Fractional powers of hyponormal operators of Putnam type.
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval
In this paper we consider a linear operator on an unbounded interval associated with a matrix linear Hamiltonian system. We characterize its Friedrichs extension in terms of the recessive system of solutions at infinity. This generalizes a similar result obtained by Marletta and Zettl for linear operators defined by even order Sturm-Liouville differential equations.
Friedrichs model operators of absolute type with one singular point.
Functional Analysis, Orthogonal Polynomials And A Theorem Of Markov.
General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators
This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.
Generalisation of Rellich's Theorem on Perturbation of (Essentially) Selfadjoin Operators.
Generalized Analytic and Quasi-Analytic Vectors
For every sequence (aₙ) of positive real numbers and an operator acting in a Banach space, we introduce the families of (aₙ)-analytic and (aₙ)-quasi-analytic vectors. We prove various properties of these families.
Generalized resolvents and spectrum for a certain class of perturbed symmetric operators.
Global existence for a Riccati equation arising in a boundary control problem for distributed parameters
Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.
Holomorphic Operator Families and Stability of Selfadjointness.
Homogeneous operators
Hypoellipticité pour une équation d'évolution abstraite du second ordre
Hypoellipticité pour une équation d'évolution abstraite du second ordre
Instabilité spectrale semiclassique pour des opérateurs non-autoadjoints I : un modèle
Dans ce travail, nous considérons un opérateur différentiel simple ainsi que des perturbations. Alors que le spectre de l’opérateur non-perturbé est confiné à une droite à l’intérieur du pseudospectre, nous montrons pour les opérateurs perturbés que les valeurs propres se distribuent à l’intérieur du pseudospectre d’après une loi de Weyl.
Invariance of Essential Spectra.
Jacobi matrices on trees
Symmetric Jacobi matrices on one sided homogeneous trees are studied. Essential selfadjointness of these matrices turns out to depend on the structure of the tree. If a tree has one end and infinitely many origin points the matrix is always essentially selfadjoint independently of the growth of its coefficients. In case a tree has one origin and infinitely many ends, the essential selfadjointness is equivalent to that of an ordinary Jacobi matrix obtained by restriction to the so called radial functions....
-uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients
L₁-uniqueness of degenerate elliptic operators
Let Ω be an open subset of with 0 ∈ Ω. Furthermore, let be a second-order partial differential operator with domain where the coefficients are real, and the coefficient matrix satisfies bounds 0 < C(x) ≤ c(|x|)I for all x ∈ Ω. If for some λ > 0 where then we establish that is L₁-unique, i.e. it has a unique L₁-extension which generates a continuous semigroup, if and only if it is Markov unique, i.e. it has a unique L₂-extension which generates a submarkovian semigroup. Moreover...
Left-definite variations of the classical Fourier expansion theorem.