Generators for quasi-free completely positive semi-groups
Generators of Brownian motions on abstract Wiener spaces
We prove that Brownian motion on an abstract Wiener space B generates a locally equicontinuous semigroup on equipped with the -topology introduced by L. Le Cam. Hence we obtain a “Laplace operator” as its infinitesimal generator. Using this Laplacian, we discuss Poisson’s equation and heat equation, and study its properties, especially the difference from the Gross Laplacian.
Generic convergence of iterates for a class of nonlinear mappings.
Generic differentiability of mappings and convex functions in Banach and locally convex spaces
Generic existence result for an eigenvalue problem with rapidly growing principal operator
We consider the eigenvalue problemin the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all are eigenvalues.
Generic existence result for an eigenvalue problem with rapidly growing principal operator
We consider the eigenvalue problem in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all λ > 0 are eigenvalues.
Generic properties of iterated function systems with place dependent probabilities.
Generic properties of learning systems
It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.
Generic properties of some boundary value problems for differential equations
Generic properties of von Kármán equations
Generic stability of the spectra for bounded linear operators on Banach spaces.
Generic well-posedness for a class of equilibrium problems.
Geometric characteristic of semi-Fredholm operators and their asymptotic behaviour
Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators
We discuss the problem of characterizing the possible asymptotic behaviour of the iterates of a sufficiently smooth nonlinear operator acting in a Banach space in small neighbourhoods of a fixed point. It turns out that under natural conditions, for the most part of initial approximations these iterates tend to "lie down" along a finite-dimensional subspace generated by the leading (peripherical) eigensubspaces of the Fréchet derivative at the fixed point and moreover the asymptotic behaviour of...
Geometric proofs of composition theorems for generalized Fourier integral operators.
Geometric properties of Banach spaces and metric fixed point theory.
Geometric properties of composition operators belonging to Schatten classes.
Geometric properties related to the fixed point property in Banach spaces.
Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces
According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof...
Géométrie du spectre dans une algèbre de Banach et domaine numérique
Dans une algèbre de Banach et dans deux cas particuliers, nous montrons la continuité du centre du plus petit disque contenant le spectre. Pour a ∈ , on donne une condition nécessaire et suffisante pour avoir où d(a) est la distance de a aux scalaires et le rayon du plus petit disque contenant K qui représente le spectre ou le domaine numérique algébrique de a. Dans un espace de Hilbert complexe, K peut représenter certains types de spectres ou de domaines numériques de a.