Distance between states and statistical inference in quantum theory
Distances between composition operators.
Composition operators Cφ induced by a selfmap φ of some set S are operators acting on a space consisting of functions on S by composition to the right with φ, that is Cφf = f º φ. In this paper, we consider the Hilbert Hardy space H2 on the open unit disk and find exact formulas for distances ||Cφ - Cψ|| between composition operators. The selfmaps φ and ψ involved in those formulas are constant, inner, or analytic selfmaps of the unit disk fixing the origin.
Distinguished Selfadjoint Extensions of Dirac Operators.
Distinguished Self-Adjoint Extensions of Dirac Operators Constructed by Means of Cutt-Off Potentials.
Distirbution of eigenvalues and nuclearity
Distortion analyticity and molecular resonance curves
Distribution semigroups on function spaces with singularities at zero.
Distribution semigroups on
Distributional fractional powers of the Laplacean. Riesz potentials
For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean...
Distributions at infinity for Riemann surfaces
Dividing measures and narrow operators
We use a new technique of measures on Boolean algebras to investigate narrow operators on vector lattices. First we prove that, under mild assumptions, every finite rank operator is strictly narrow (before it was known that such operators are narrow). Then we show that every order continuous operator from an atomless vector lattice to a purely atomic one is order narrow. This explains in what sense the vector lattice structure of an atomless vector lattice given by an unconditional basis is far...
Does Kirk's theorem hold for multivalued nonexpansive mappings?
Does Newton's method for set-valued maps converges uniformly in mild differentiability context?
Domain characterizations of certain functions of power-bounded operators
We create a general framework for describing domains of functions of power-bounded operators given by power series with log-convex coefficients. This sheds new light on recent results of Assani, Derriennic, Lin and others. In particular, we resolve an open problem regarding the "one-sided ergodic Hilbert transform" formulated in a 2001 paper by Derriennic and Lin.
Domain perturbations, capacity and shift of eigenvalues
After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator . If is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in Capacity in abstract Hilbert spaces and applications to higher order differential operators (Comm. P. D. E., 24:759–775,...
Domaine de la racine carrée de certains opérateurs différentiels accrétifs
Les racines carrées d’opérateurs différentiels accrétifs ont été définies et étudiées par Kato. Dans le cas d’opérateurs différentiels à coefficients , les racines carrées sont des opérateurs pseudo-différentiels. Le cas des opérateurs différentiels à coefficients mesurables et bornés conduit à des racines carrées au-delà des opérateurs pseudo-différentiels. Ces nouveaux opérateurs s’étudient grâce à des mesures de Carleson.
Domaine numérique de l'opérateur produit M2,A,B et de la dérivation généralisée δ2,A,B.
Domaine Numérique du produit AB avec A normal
2000 Mathematics Subject Classification: 18B30, 47A12.Let A, B be two linear operators on a complex Hilbert space H. We extend a Bouldin's result (1969) conserning W(AB) - the numerical range of the product AB. We show, when AB = BA and A is normal, than W(AB).
Dominant eigenvalue problem for positive integral operators and its solution by Monte Carlo method
In this paper, a method of numerical solution to the dominant eigenvalue problem for positive integral operators is presented. This method is based on results of the theory of positive operators developed by Krein and Rutman. The problem is solved by Monte Carlo method constructing random variables in such a way that differences between results obtained and the exact ones would be arbitrarily small. Some numerical results are shown.
Dominated ergodic theorems in rearrangement invariant spaces
We study conditions under which Dominated Ergodic Theorems hold in rearrangement invariant spaces. Consequences for Orlicz and Lorentz spaces are given. In particular, our results generalize the classical theorems for the spaces and the classes .