Extensions of operators and the Dirichlet problem in potential theory
Extensions of the representation theorems of Riesz and Fréchet
We present two types of representation theorems: one for linear continuous operators on space of Banach valued regulated functions of several real variables and the other for bilinear continuous operators on cartesian products of spaces of regulated functions of a real variable taking values on Banach spaces. We use generalizations of the notions of functions of bounded variation in the sense of Vitali and Fréchet and the Riemann-Stieltjes-Dushnik or interior integral. A few applications using geometry...
Extreme Boundaries and continous affine functions.
Facial Topologies for Subspaces of C(X).
Factoring Operators Through Banach Lattices Not Containing C(0, 1).
Fatou's Lemma and the Lebesgue's Convergence Theorem
In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015
Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions
We characterize finite codimensional linear isometries on two spaces, C (n)[0; 1] and Lip [0; 1], where C (n)[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C (n)[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.
Fixpunktsatz und monotone Lösungen der Differentialgleichung
Fonctionnelles analytiques sur certains espaces de Banach
Il est démontré que l’espace des fonctions holomorphes sur un sous-espace homogène , au sens de Katznelson, de muni de la topologie engendrée par les semi-normes portées par les compacts de , est bornologique.
Fourier Transforms of Lipschitz Functions and Fourier Multipliers on Compact Groups.
Fractal functions and Schauder bases
Funciones unimodulares y acotación uniforme.
In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H∞ with the weak-star topology.
Functional differential equations of the Cauchy-Kowalewsky type.
Functional properties of C(X) and chain conditions on X
Functional-analytic properties of Corson-compact spaces
Generalized centers of finite sets in Banach spaces.
Generalized Helly spaces, continuity of monotone functions, and metrizing maps
Given an ordered metric space (in particular, a Banach lattice) E, the generalized Helly space H(E) is the set of all increasing functions from the interval [0,1] to E considered with the topology of pointwise convergence, and E is said to have property (λ) if each of these functions has only countably many points of discontinuity. The main objective of the paper is to study those ordered metric spaces C(K,E), where K is a compact space, that have property (λ). In doing so, the guiding idea comes...
Generalized Hölder type spaces of harmonic functions in the unit ball and half space
We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity and the second is the variable exponent harmonic Hölder space with the continuity modulus . We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.
Generalized weak peripheral multiplicativity in algebras of Lipschitz functions
Let (X, d X) and (Y,d Y) be pointed compact metric spaces with distinguished base points e X and e Y. The Banach algebra of all -valued Lipschitz functions on X - where is either‒or ℝ - that map the base point e X to 0 is denoted by Lip0(X). The peripheral range of a function f ∈ Lip0(X) is the set Ranµ(f) = f(x): |f(x)| = ‖f‖∞ of range values of maximum modulus. We prove that if T 1, T 2: Lip0(X) → Lip0(Y) and S 1, S 2: Lip0(X) → Lip0(X) are surjective mappings such that for all f, g ∈ Lip0(X),...
Generation of analytic semigroups by elliptic operators of second order in Hölder spaces