The Dirichlet problem for Baire-one functions

Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.     

On the apostol-bernoulli polynomials

In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161–167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications.     

A priori estimates of strong solutions of semilinear parabolic equations

We study an initial boundary value problem for the semilinear parabolic equation

Characterizations of spaces in the unit ball of

Let B denote the unit ball of . For 0<p<∞, the holomorphic function spaces Q_p and Q_p,0 on the unit ball of are defined as

and

In this paper, we give some derivative-free, mixture and oscillation characterizations for Q_p and Q_p,0 spaces in the unit ball of .     

Equivalent Norms in Spaces of Functions of Fractional Smoothness on Arbitrary Domains

In this paper, we study the spaces B _pq ^s (G) and L _pq ^s (G) of functions f with positive exponent of smoothness s > 0 given on a domain . The norms on these spaces are defined via integral norms of the difference of the function f of order m > s treated as a function of the point of the domain and of the difference increment. For an arbitrary domain , we characterize these spaces in terms of the local approximations of the function by polynomials of degree m – 1.     

On -topological vector spaces generated by a co-tower of L-topological vector spaces

In this paper, a characterization for an I(L)-topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I(L)-topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I(L)-topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I(L)-topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too.     

The Coordinatewise Uniformly Kadec–Klee Property in Some Banach Spaces

We introduce a new property UKK _c for a Banach space and show for an Orlicz sequence space the following: UKK _c H _{c 2}.     

Cohomologie <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> en degré 1 des espaces homogènes

The L ^p -cohomology in degree 1 of Riemannian homogeneous spaces is computed. It turns out that reduced cohomology does not vanish exactly for spaces quasiisometric to negatively curved homogeneous spaces.      

Algebras and Spaces of Dense Constancies

A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f C(X) there is a family of open sets {U _i : i I}, the union of which is dense in X, such that f, restricted to each U _i , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property.     

Dense Families of Selections and Finite-Dimensional Spaces

A characterization of n-dimensional spaces via continuous selections avoiding Z _n -sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrand's theorem, and to obtain a new alternative proof of the Hurewicz formula. It is also shown that our selection theorem yields an easy proof of a Michael's result.     

D-boundedness andD-compactness in finite dimensional probabilistic normed spaces

In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion ofD-compactness and D-boundedness in probabilistic normed spaces.     

p-Banach Spaces and p-Totally Convex Spaces. II

We show that the results about the set S : ={ [0, 1] ^{1 / p} x + (1 – )^{1 / p} z ^{1 / p} y + (1 – )^{1 / p} z}, where x, y, z elements of a p-absolutely convex space D and `' is a congruence relation on D are the best possible. Finally, we give an explicit construction of the left adjoint of the comparison functor Ô _p : B an _p T C _p (resp. Ô _{p, fin} : V ec _p A C _p ).     

On fuzzy covering properties

The purpose of this paper is to introduce properties of the notion of α-compactness for fuzzy topological spaces. Moreover, α _c-compact spaces are introduced and properties of them are also discussed for fuzzy topological spaces.      

A pointwise ergodic theorem for contractions in \mathbb{L}_p (ℋ)-spaces

We consider L _p -spaces of measurable functions ranging in a Hilbert space and single out a class of contractions on such spaces for which the pointwise ergodic theorem holds.     

On a family of vector space categories

In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.     

Compact Hopf hypersurfaces of constant mean curvature in complex space forms

We prove that every connected compact Hopf hypersurface of a complex space form, contained in a geodesic ball of radius strictly smaller than the injectivity radius of, having constant mean curvature and with if if < 0 is a geodesic sphere of.Work partially supported by DGICYT Grant No. PB91-0324.     

Domestic iterated one-point extensions of algebras by two-ray modules

In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large global dimensions.     

Convexity properties of coverings of 1-convex manifolds

We show the following result: let X be a 1-convex manifold, A its exceptional set, k = dimA and p : Y → X any covering. Then Y can be exhausted by an increasing sequence of smoothly bounded k-convex domains.      

p-Frames in Separable Banach Spaces

Let X be a separable Banach space with dual X ^*. A countable family of elements {g _i }X ^* is a p-frame (1 p ) if the norm _X is equivalent to the ^p -norm of the sequence {g _i ()}. Without further assumptions, we prove that a p-frame allows every gX ^* to be represented as an unconditionally convergent series g=d _i g _i for coefficients {d _i } ^q , where 1/p+1/q=1. A p-frame {g _i } is not necessarily linear independent, so {g _i } is some kind of overcomplete basis for X ^*. We prove that a q-Riesz basis for X ^* is a p-frame for X and that the associated coefficient functionals {f _i } constitutes a p-Riesz basis allowing us to expand every fX (respectively gX ^*) as f=g _i (f)f _i (respectively g=g(f _i )g _i ). In the general case of a p-frame such expansions are only possible under extra assumptions.     

On Some Properties of Randomly Indexed Sequences of Random Elements

Let be a probability space with a nonatomic measure P and let (S,ρ) be a separable complete metric space. Let {N _n ,n≥1} be an arbitrary sequence of positive-integer valued random variables. Let {F _k ,k≥1} be a family of probability laws and let X be some random element defined on and taking values in (S,ρ). In this paper we present necessary and sufficient conditions under which one can construct an array of random elements {X _n,k ,n,k≥1} defined on the same probability space and taking values in (S,ρ), and such that , and moreover as  n→∞. Furthermore, we consider the speed of convergence to X as n→∞.