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Extensions from the Sobolev spaces $H^{1}$ satisfying prescribed Dirichlet boundary conditions

Alexander Ženíšek (2004)

Applications of Mathematics

Extensions from $H^{1} (Ω_{P})$ into $H^{1} (Ω)$ (where $Ω_{P} \subset Ω$ ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary $\partial Ω$ of $Ω$ . The corresponding extension operator is linear and bounded.

Extensions of basic sequences in Fréchet spaces

William Robinson (1973)

Studia Mathematica

Extensions of certain real rank zero $C^{*}$ -algebras

Marius Dadarlat, Terry A. Loring (1994)

Annales de l'institut Fourier

G. Elliott extended the classification theory of $A F$ -algebras to certain real rank zero inductive limits of subhomogeneous $C^{*}$ -algebras with one dimensional spectrum. We show that this class of $C^{*}$ -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the $K_{1}$ -group. Perturbation and lifting results are provided for certain subhomogeneous $C^{*}$ -algebras.

Extensions of compact continuous maps into decomposable sets

L. Faina (1991)

Rendiconti del Seminario Matematico della Università di Padova

Extensions of continuous functions into locally convex spaces over non-Archimedean fields

Robert L. Ellis (1971)

Colloquium Mathematicae

Extensions of convex functionals on convex cones

E. Ignaczak, A. Paszkiewicz (1998)

Applicationes Mathematicae

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.