μ-Separations in generalized topological spaces

This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0,1,2,3,4, μTD-spaces and μR0-spaces are obtained and some relations among these spaces are established.     

ζ μ -sets in generalized topological spaces

We define ζ _μ -sets, (ζ,μ)-closed sets and generalized ζ _μ -sets in a generalized topological space and investigate properties of several low separation axioms of generalized topologies constructed by the families of these sets. Characterizations of some properties of (ζ,μ)-R ₀ and (ζ,μ)-R ₁ generalized topological spaces will be given.     

Factorization in generalized Calogero–Moser spaces

Using a recent construction of Bezrukavnikov and Etingof, [R. Bezrukavnikov, P. Etingof, Induction and restriction functors for rational Cherednik algebras, arXiv: 0803.3639], we prove that there is a factorization of the Etingof–Ginzburg sheaf on the generalized Calogero–Moser space associated to a complex reflection group. In the case $W=S_n$, this confirms a conjecture of Etingof and Ginzburg, [P. Etingof, V. Ginzburg, Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphisms, Invent. Math 147 (2002) 243–348].     

Jackson’s theorem in Q_p spaces

A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p ∞, a 1, and k-1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an absolute constant depending only on the parameter a.     

Denting points in K?the-Bochner spaces

A characterization of denting points in the unit ball of Köthe-Bochner spaceE(X) is given. This characterization is a generalization of some analogous theorems for Bochner and Musielak Orlicz spaces and it is compared to similar known results concerning strongly extreme points inE(X).Scholar of Ministere de la Recherche et de la Technologie of France, while on leave from Technical University at Pozna, Poland.     

Composition operators in Orlicz–Sobolev spaces

We obtain necessary and sufficient conditions for a homeomorphism of domains in a Euclidean space to generate a bounded embedding operator of the Orlicz–Sobolev spaces defined by a special class of N-functions.     

Tubes in three–dimensional projective spaces

A partial tube in PG(3, q) is a pair , where is a collection of mutually disjoint lines of PG(3, q) with the property that for each plane π of PG(3, q) through L, the intersection of π with the lines of is an arc. Here, we generalize the notion of partial tube allowing the ground field to be any algebraically closed field. To a generalized partial tube we will associate an irreducible surface of degree d in providing upper bounds on d. The authors were partially supported by MIUR and GNSAGA of INdAM (Italy).     

Backward–backward splitting in Hadamard spaces

The backward–backward algorithm is a tool for finding minima of a regularization of the sum of two convex functions in Hilbert spaces. We generalize this setting to Hadamard spaces and prove the convergence of an error-tolerant version of the backward–backward method.     

On angles in Teichmüller spaces

We discuss the existence of the angle between two curves in Teichmüller spaces and show that, in any infinite dimensional Teichmüller space, there exist infinitely many geodesic triangles each of which has the same three vertices and satisfies the property that its three sides have the same and arbitrarily given length while its three angles are equal to any given three possibly different numbers from 0 to $\pi $ . This implies that the sum of three angles of a geodesic triangle may be equal to any given number from 0 to $3\pi $ in an infinite dimensional Teichmüller space.     

Interpolation operators in Orlicz–Sobolev spaces

We study classical interpolation operators for finite elements, like the Scott–Zhang operator, in the context of Orlicz–Sobolev spaces. Furthermore, we show estimates for these operators with respect to quasi-norms which appear in the study of systems of p-Laplace type.     

Bernstein bases in Müntz spaces

Extended Chebyshev spaces possess Bernstein type bases. In this paper, we determine the expressions of such bases in spaces spanned by the constants and power functions with consecutive integer exponents. This revised version was published online in August 2006 with corrections to the Cover Date.     

Metric betweenness,Ptolemaic spaces,and isometric embeddings of pretangent spaces in ℝ

We study some properties of pretangent spaces describing the infinitesimal geometry of general metric spaces. The necessary and sufficient conditions characterizing Ptolemaic pretangent spaces and pretangent spaces, where every three points are situated “on a single straight line,” are found. As a corollary, we obtain a criterion of embeddability of pretangent spaces into the set ℝ of real numbers endowed by the natural metric.     

Maslov’s canonical operator in abstract spaces

Recently, a number of new methods for constructing asymptotic solutions to various evolution equations has been developed. These asymptotic solutions are expressed at each instant of time via an elementy of some smooth manifoldy and an elementf of some Hilbert space . We study general properties of the mapping that assigns an asymptotic formula to the pair (y, f). Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 437–456, March, 1999.     

Quasiconvex variational functionals in Orlicz–Sobolev spaces

We prove a C ^1,α partial regularity result for minimizers of variational integrals of the type $$ J[u]:=\int\limits_\Omega f(\nabla u){\rm d}x, \, \, u:\Omega\subset \mathbb{R}^n \to \mathbb{R}^N, $$ where the integrand f is strictly quasiconvex and satisfies suitable growth conditions in terms of Young functions.     

Composition operators between Bloch-type spaces in the polydisc

We characterize those holomorphic mappings (?) from the polydisc Dn in Cn to itself for which the induced composition operators C(?) are bounded (or compact) from the Bloch-type space Bωto Bμ(respectively, from the little Bloch-type space Bω,0 to Bμ,0), where ωis a normal function on [0,1) and μis a nonnegative function on [0,1) with μ(tn) > 0 for some sequence {tn}n=1∞(?)[0,1) satisfying limn→∞tn = 1.     

Convolution operators in discrete Cesàro spaces

Archiv der Mathematik - The discrete Cesàro spaces $${{\text {ces(p )}}}, 1< p < \infty ,$$ are well known and arise from the classical sequence spaces $$\ell ^p,1<\infty...