Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings.
Characterizations of -stratifiable spaces
Characterizing dominates on a family of triangular norms.
Characterizing Optimality in Nonconvex Optimizationi
Charakterisierungen von nirgends differenzierbaren Weierstraß-Funktionen durch Replikativität.
Chebyshev inequalities and self-dual cones.
Choosing roots of polynomials with symmetries smoothly.
Classes of Weighted Symmetric Functions
Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives
This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...
Classifications and characterizations of Baire-1 functions
Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space , to the subclasses , . In [8], for every ordinal we define a new type of convergence for sequences of real-valued functions (-uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric space , and...
Closed universal subspaces of spaces of infinitely differentiable functions
We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace...
Cluster directions of euclidean sets
Cluster sets of arbitrary functions defined on plane sets
Coefficient inequalities for certain classes of analytic and univalent functions.
Comments on some analytic inequalities.
Commuting functions and simultaneous Abel equations
The system of Abel equations α(ft(x)) = α(x) + λ(t), t ∈ T, is studied under the general assumption that are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.
Compact and weakly compact homomorphisms between algebras of differentiable functions.
Many authors have recently studied compact and weakly compact homomorphisms between function algebras. Among them, Lindström and Llavona [2] treat weakly compact continuous homomorphisms between algebras of type C(T) when T is a completely regular Hausdorff space.Llavona asked wether the results in [2] are valid in the case of algebras of differentiable functions on Banach spaces. The purpose of this note is to give an affirmative answer to this question, by proving that weakly compact homomorphisms...
Compact imbeddings in weighted Sobolev spaces and nonlinear boundary value problems
Compact operators and integral equations in the space
The space of Henstock-Kurzweil integrable functions on is the uncountable union of Fréchet spaces . In this paper, on each Fréchet space , an -norm is defined for a continuous linear operator. Hence, many important results in functional analysis, like the Banach-Steinhaus theorem, the open mapping theorem and the closed graph theorem, hold for the space. It is known that every control-convergent sequence in the space always belongs to a space for some . We illustrate how to apply results...