Extension of vector measures
Extension of vector-valued holomorphic and harmonic functions
We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.
Extension operators for analytic functions defined on certain closed subvarieties of a Stein space
Extension operators on balls and on spaces of finite sets
We study extension operators between spaces of continuous functions on the spaces of subsets of X of cardinality at most n. As an application, we show that if is the unit ball of a nonseparable Hilbert space H equipped with the weak topology, then, for any 0 < λ < μ, there is no extension operator .
Extension techniques in -cross products by compact group duals and in quantum field theory.
Extension theorems (vector measures on quantum logics)
Extension theory for Sobolev spaces on open sets with Lipschitz boundaries
Extension via interpolation
We suggest a modification of the Pawłucki and Pleśniak method to construct a continuous linear extension operator by means of interpolation polynomials. As an illustration we present explicitly the extension operator for the space of Whitney functions given on the Cantor ternary set.
Extensiones finitogeneradas y proyectivas de un álgebra m-convexa.
Extensions and Selections in Subspaces of C(K).
Extensions by mollifiers in Basov spaces
Extensions de jets dans des intersections de classes non quasi-analytiques
In [3], J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset E of ℝⁿ, in the case of intersections of non-quasi-analytic classes with moderate growth and a Łojasiewicz theorem in the regular situation. These intersections are included in the intersection of Gevrey classes. Here we prove an extension theorem in the case of more general intersections such that every -Whitney jet belongs to one of them. We also prove a linear extension theorem...
Extensions de systèmes dynamiques par des endomorphismes de groupes compacts
Extensions des -algèbres
Extensions from the Sobolev spaces satisfying prescribed Dirichlet boundary conditions
Extensions from into (where ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded.
Extensions of basic sequences in Fréchet spaces
Extensions of certain real rank zero -algebras
G. Elliott extended the classification theory of -algebras to certain real rank zero inductive limits of subhomogeneous -algebras with one dimensional spectrum. We show that this class of -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the -group. Perturbation and lifting results are provided for certain subhomogeneous -algebras.
Extensions of compact continuous maps into decomposable sets
Extensions of continuous functions into locally convex spaces over non-Archimedean fields
Extensions of convex functionals on convex cones
We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.