Search results for "Operator theory"
showing 10 items of 95 documents
On essential maximality of linear pseudo-differential operators
1989
On Determinants of Integrable Operators with Shifts
2013
Integrable integral operator can be studied by means of a matrix Riemann--Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Riemann--Hilbert problem becomes operator valued and this complicates strongly the analysis. In this note, we show how to circumvent, in a very simple way, the use of such a setting while still being able to characterize the large-$x$ asymptotic behavior of the determinant associated with the operator.
Newton algorithm for Hamiltonian characterization in quantum control
2014
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown paramete…
Maximal Operators with Respect to the Numerical Range
2018
Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $\mathfrak{n}$-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
Monotony Based Imaging in EIT
2010
We consider the problem of determining conductivity anomalies inside a body from voltage‐current measurements on its surface. By combining the monotonicity method of Tamburrino and Rubinacci with the concept of localized potentials, we derive a new imaging method that is capable of reconstructing the exact (outer) shape of the anomalies. We furthermore show that the method can be implemented without solving any non‐homogeneous forward problems and show a first numerical result.
On essential spectra of operator-matrices and their Feshbach maps
2004
Abstract A connection between the essential spectrum of certain operator-matrices and essential spectra of the corresponding “Feshbach maps” is discussed and applied to some concrete rational operator-valued functions.
Singular Neumann (p, q)-equations
2019
We consider a nonlinear parametric Neumann problem driven by the sum of a p-Laplacian and of a q-Laplacian and exhibiting in the reaction the competing effects of a singular term and of a resonant term. Using variational methods together with suitable truncation and comparison techniques, we show that for small values of the parameter the problem has at least two positive smooth solutions.
Factorization of strongly (p,sigma)-continuous multilinear operators
2013
We introduce the new ideal of strongly-continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal - which is also new for the linear case - is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.
Property (w) for perturbations of polaroid operators
2008
Abstract A bounded linear operator T ∈ L ( X ) acting on a Banach space satisfies property ( w ) , a variant of Weyl’s theorem, if the complement in the approximate point spectrum σ a ( T ) of the Weyl essential approximate-point spectrum σ wa ( T ) is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property ( w ) for a polaroid operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T.
Operators which have a closed quasi-nilpotent part
2002
We find several conditions for the quasi-nilpotent part of a bounded operator acting on a Banach space to be closed. Most of these conditions are established for semi-Fredholm operators or, more generally, for operators which admit a generalized Kato decomposition. For these operators the property of having a closed quasi-nilpotent part is related to the so-called single valued extension property.