Geometry of nuclear spaces - I
Geometry of nuclear spaces. II - Linear topological invariants
Geometry of nuclear spaces. III - Spaces of holomorphic functions
Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I.
Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. II.
Gliding hump properties and some applications.
Greedy Approximation with Regard to Bases and General Minimal Systems
*This research was supported by the National Science Foundation Grant DMS 0200187 and by ONR Grant N00014-96-1-1003This paper is a survey which also contains some new results on the nonlinear approximation with regard to a basis or, more generally, with regard to a minimal system. Approximation takes place in a Banach or in a quasi-Banach space. The last decade was very successful in studying nonlinear approximation. This was motivated by numerous applications. Nonlinear approximation is important...
Growth Properties of Pseudo-Convex Domains and Domains of Holomorphy in Locally Convex Topological Vector Spaces.
-BMO duality on graphs
On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space is equal to , and therefore that its dual is BMO. We also prove the atomic decomposition for for p ≤ 1 close enough to 1.
Hahn-Banach theorem implies Riesz theorem.
Hahn-Banach Type Theorems for Hypolinear Functionals.
Harmonic interpolating sequences, and BMO
Let be a sequence in the upper half plane. If and ifhas solution in the class of Poisson integrals of functions for any sequence , then we show that is an interpolating sequence for . If , has solution in the class of Poisson integrals of BMO functions whenever , then is again an interpolating sequence for . A somewhat more general theorem is also proved and a counterexample for the case is described.
Hausdorff Matrices as Bounded Operators over lp.
Hille-Yosida theory in convenient analysis.
A Hille-Yosida Theorem is proved on convenient vector spaces, a class, which contains all sequentially complete locally convex spaces. The approach is governed by convenient analysis and the credo that many reasonable questions concerning strongly continuous semigroups can be proved on the subspace of smooth vectors. Examples from literature are reconsidered by these simpler methods and some applications to the theory of infinite dimensional heat equations are given.
Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces
We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2,...
Holomorphic Functions and the (BB)-Property.
Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces
Holomorphic Functions on (c0, Xb)-Modules.
Holomorphic functions on Fréchet spaces with Schauder basis.
Holomorphic functions on fully nuclear spaces