Extended stability problem for alternative Cauchy-Jensen mappings.
Extenders for vector-valued functions
Given a subset A of a topological space X, a locally convex space Y, and a family ℂ of subsets of Y we study the problem of the existence of a linear ℂ-extender , which is a linear operator extending bounded continuous functions f: A → C ⊂ Y, C ∈ ℂ, to bounded continuous functions f̅ = u(f): X → C ⊂ Y. Two necessary conditions for the existence of such an extender are found in terms of a topological game, which is a modification of the classical strong Choquet game. The results obtained allow us...
Extendibility of polynomials and analytic functions on
We prove that extendible 2-homogeneous polynomials on spaces with cotype 2 are integral. This allows us to find examples of approximable non-extendible polynomials on (1 ≤ p < ∞ ) of any degree. We also exhibit non-nuclear extendible polynomials for 4 < p < ∞. We study the extendibility of analytic functions on Banach spaces and show the existence of functions of infinite radius of convergence whose coefficients are finite type polynomials but which fail to be extendible.
Extending a Norm from a Vector Lattice to its Dedekind Completion.
Extending and lifting some linear topological structures.
Extending holomorphic maps from compact sets in infinite dimensions
Extending holomorphic maps in infinite dimensions
Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in...
Extending hypersurfaces and meromorphic functions.
Extending traces to factorial traces.
Extension and decomposition operators in products of strictly pseudoconvex sets
Extension and lacunas of solutions of linear partial differential equations
Let be compact, convex sets in with and let be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of in the space of all -functions on extends to a zero solution in resp. in . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of in and in terms of fundamental solutions for with lacunas.
Extension and lifting of weakly continuous polynomials
We show that a Banach space X is an ℒ₁-space (respectively, an -space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an -space.
Extension and splitting theorems for Fréchet spaces of type 2.
We prove the following common generalization of Maurey's extension theorem and Vogt's (DN)-(Omega) splitting theorem for Fréchet spaces: if T is an operator from a subspace E of a Fréchet space G of type 2 to a Fréchet space F of dual type 2, then T extends to a map from G into F'' whenever G/E satisfies (DN) and F satisfies (Omega).
Extension de la catégorie des algèbres de Kac
On munit la classe des algèbres de Kac d’une nouvelle classe de morphismes, stable par dualité. Cela permet de rendre compte, dans les cas abélien ou symétrique, de la catégorie des groupes localement compacts munis des morphismes continus de groupe. Le lien avec les morphismes précédemment définis et beaucoup plus restrictifs est établi.
Extension d'un Théorème de Harte et Applications aux Algèbres de Jordan-Banach.
Extension d'un théorème de von Neumann dans les a*-algèbres.
Extension Gevrey et rigidité dans un secteur
We study a rigidity property, at the vertex of some plane sector, for Gevrey classes of holomorphic functions in the sector. For this purpose, we prove a linear continuous version of Borel-Ritt's theorem with Gevrey conditions
Extension maps in ultradifferentiable and ultraholomorphic function spaces
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
Extension of algebra norms and applications
Extension of Analytic Functional Calculus Mappings and Duality by ...-Closed Forms with Growth.