Статьи журнала - Владикавказский математический журнал
Все статьи: 983
On extreme extension of positive operators
Статья научная
Given vector lattices E, F and a positive operator S from a majorzing subspace D of E to F, denote by E(S) the collection of all positive extensions of S to all of E. This note aims to describe the collection of extreme points of the convex set E(T∘S). It is proved, in particular, that E(T∘S) and T∘E(S) coincide and every extreme point of E(T∘S) is an extreme point of T∘E(S), whenever T:F→G is a Maharam operator between Dedekind complete vector lattices. The proofs of the main results are based on the three ingredients: a characterization of extreme points of subdifferentials, abstract disintegration in Kantorovich spaces, and an intrinsic characterization of subdifferentials.
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On finite homogeneous metric spaces
Статья научная
This survey is devoted to recently obtained results on finite homogeneous metric spaces. The main subject of discussion is the classification of regular and semiregular polytopes in Euclidean spaces by whether or not their vertex sets have the normal homogeneity property or the Clifford - Wolf homogeneity property. Every finite homogeneous metric subspace of an Euclidean space represents the vertex set of a compact convex polytope with the isometry group that is transitive on the set of vertices, moreover, all these vertices lie on some sphere. Consequently, the study of such subsets is closely related to the theory of convex polytopes in Euclidean spaces. The normal generalized homogeneity and the Clifford - Wolf homogeneity describe more stronger properties than the homogeneity. Therefore, it is natural to first check the presence of these properties for the vertex sets of regular and semiregular polytopes. In addition to the classification results, the paper contains a description of the main tools for the study of the relevant objects.
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On generalization of Fourier and Hartley transforms for some quotient class of sequences
Статья научная
In this paper we consider a class of distributions and generate two spaces of Boehmians for certain class of integral operators. We derive a convolution theorem and generate two spaces of Boehmians. The integral operator under concern is well-defined, linear and one-to-one in the class of Boehmians. An inverse problem is also discussed in some details.
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On generalized Kenmotsu manifolds as hypersurfaces of Vaisman-Gray manifolds
Статья научная
In this paper, we conclude that the hypersurfaces of Vaisman-Gray manifolds have generalized Kenmotsu structures under some conditions for the Lee form, Kirichenko's tensors and the second fundamental form of the immersion of the hypersurface into the manifold of Vaisman-Gray class. Moreover, the components of the second fundamental form are determined when the foregoing hypersurfaces have generalized Kenmotsu structures or any special kind of it or Kenmotsu structures, such that some of these components are vanish. Also, some components of Lee form and some components of some Kirichenko's tensors in the Vaisman-Gray class are equal to zero. On the other hand, the minimality of totally umbilical, totally geodesic hypersurfaces of Vaisman-Gray manifolds with generalized Kenmotsu structures are investigated. In addition, we deduced that the hypersurface of Vaisman-Gray manifold that have generalized Kenmotsu structure is totally geodesic if and only if it is totally umbilical and some components of Lee form are constants.
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On ideal of compact operators in real factors
Статья научная
In the present paper the real ideals of relatively compact operators of W*-algebras are considered. A description (up to isomorphism) of real two-sided ideal of relatively compact operators of the complex W*-factors is given.
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On meromorphic function with maximal deficiency sum and it's difference operators
Статья научная
The paper deals with characteristic funtion and deficiency of a meromorphic function. We mainly focused on the relation between the characteristic function of a product of difference operators with the characteristic function of a meromorphic function with maximal deficiency sum. The concept of maximal deficiency sum of a meromorphic function is employed as an effective tool for our research. In the same context, the notion of a difference polynomial of a difference operator is discussed. The paper contains the details analysis and discussion of some asymptotic behaviour of the product of difference operators, such as limr→∞T(r,∏qi=1Δηif)T(r,f), limr→∞N(r,0;∏qi=1Δηif)T(r,∏qi=1Δηif), lim r→∞N(r,∞;∏qi=1Δηif)+N(r,0;∏qi=1Δηif)T(r,∏qi=1Δηif) etc. and same resolution and discussion also developed for the difference polynomial of difference operators. Several innovative idea to establish some inequalities on the zeros and poles for ∏qi=1Δηif and L(Δηf) are also introduced. We broadly elaborate our results with many remarks and corollaries, and give two excellent examples for proper justification of our results. The results on product and polynomial of difference operators of our article improved and generalised the results of Z. Wu.
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On minimax theorems for sets closed in measure
Статья научная
This article is devoted to the Ky Fan minimax theorem for convex sets closed in measure in L^1. In general, these sets do not carry any formal compactness properties for any reasonable topology.
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On neveu decomposition and ergodic type theorems for semi-finite von Neumann algebras
Статья научная
Some ergodic type theorems for automorphisms of semi-finite von Neumann algebras are considered. Neveu decomposition is employed in order to prove stochastical convergence. This work is a generalization of authors results from [5] to the case of semi-finite von Neumann algebras.
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On non-commutative ergodic type theorems for free finitely generated semigroups
Статья научная
In the paper the authors generalize Bufetov's Ergodic Type Theorems to the case of the actions of free finitely generated semigroups on von Neumann algebras.
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On normal subgroups of the group representation of the Cayley tree
Статья научная
Gibbs measure plays an important role in statistical mechanics. On a Cayley tree, for describing periodic Gibbs measures for models in statistical mechanics we need subgroups of the group representation of the Cayley tree. A normal subgroup of the group representation of the Cayley tree keeps the invariance property which is a significant tool in finding Gibbs measures. By this occasion, a full description of normal subgroups of the group representation of the Cayley tree is a significant problem in Gibbs measure theory. For instance, in [1, 2] a full description of normal subgroups of indices four, six, eight, and ten for the group representation of a Cayley tree is given. The present paper is a generalization of these papers, i. e., in this paper, for any odd prime number p, we give a characterization of the normal subgroups of indices 2n, n∈{p,2p} and 2i,i∈N, of the group representation of the Cayley tree.
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On positive invertibility and splittings of operators in ordered Banach spaces
Статья научная
The positive invertibility of operators between Banach spaces, ordered by special closed cones, is characterized by the existence of splittings for the operators into the difference of two operators with appropriate spectral properties. Some results, up to now known only for matrices, are generalized to operators and to order intervals of operators.
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On projective limits of real C*-algebras and Jordan operator algebras
Статья научная
In the present paper a real and Jordan analogues of complex locally C*-algebras are introduced. Their definitions and basic properties are discussed.
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On some properties of extensions of commutative unital rings
Статья научная
We find necessary and sufficient conditions for the ring R[α] to be either a field or a domain whenever R is a commutative ring with 1 and α is an algebraic element over R. This continues the studies started by Nachev (Compt. Rend. Acad. Bulg. Sci., 2004) and (Commun. Alg., 2005) as well as their generalization due to Mihovski (Compt. Rend. Acad. Bulg. Sci., 2005).
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On some properties of orthosymmetric bilinear operators
Статья научная
This note contains some properties of positive orthosymmetric bilinear operators on vector lattices which are well known for almost f-algebra multiplication but despite of their simplicity does not seem appeared in the literature.
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On stability of retro Banach frame with respect to b-linear functional in n-Banach space
Статья научная
We introduce the notion of a retro Banach frame relative to a bounded b-linear functional in n-Banach space and see that the sum of two retro Banach frames in n-Banach space with different reconstructions operators is also a retro Banach frame in n-Banach space. Also, we define retro Banach Bessel sequence with respect to a bounded b-linear functional in n-Banach space. A necessary and sufficient condition for the stability of retro Banach frame with respect to bounded b-linear functional in n-Banach space is being obtained. Further, we prove that retro Banach frame with respect to bounded b-linear functional in n-Banach space is stable under perturbation of frame elements by positively confined sequence of scalars. In n-Banach space, some perturbation results of retro Banach frame with the help of bounded b-linear functional in n-Banach space have been studied. Finally, we give a sufficient condition for finite sum of retro Banach frames to be a retro Banach frame in n-Banach space. At the end, we discuss retro Banach frame with respect to a bounded b-linear functional in Cartesian product of two n-Banach spaces.
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On the Gehring type condition and properties of mappings
Статья научная
The goal of this work is to obtain an analytical description of mappings satisfying some capacity inequality (so called Gp-condition): we study mappings for which the Gp-condition holds for a cubical ring. In other words, we replace rings with concentric spheres in the Gp-condition by rings with concentric cubes. We obtain new analytic properties of homeomophisms in Rn meeting Gehring type capacity inequality. In this paper the capacity inequality means that the capacity of the image of a cubical ring is controlled by the capacity of the given ring. From the analytic properties we conclude some geometric properties of mappings under consideration. The method is new and is based on an equivalent analytical description of such mappings previously established by the author. Our arguments are based on assertions and methods discovered in author's recent papers [1] and [2] (see also some references inside). Then we obtain geometric properties of these mappings.
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On the balanced subgroups of modular group rings
Статья научная
The balanced property of certain subgroups of the group of all normalized p-torsion invertible elements in a modular group ring of characteristic p is explored.
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On the expansions of analytic functions on convex locally closed sets in exponential series
Статья научная
Let Q be a bounded, convex, locally closed subset of CN with nonempty interior. For N>1 sufficient conditions are obtained that an operator of the representation of analytic functions on Q by exponential series has a continuous linear right inverse. For N=1 the criterions for the existence of a continuous linear right inverse for the representation operator are proved
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On the rate of convergence of ergodic averages for functions of Gordin space
Статья научная
For an automorphisms with non-zero Kolmogorov-Sinai entropy, a new class of L2-functions called the Gordin space is considered. This space is the linear span of Gordin classes constructed by some automorphism-invariant filtration of σ-algebras Fn. A function from the Gordin class is an orthogonal projection with respect to the operator I-E(⋅|Fn) of some Fm-measurable function. After Gordin's work on the use of the martingale method to prove the central limit theorem, this construction was developed in the works of Voln\'{y}. In this review article we consider this construction in ergodic theory. It is shown that the rate of convergence of ergodic averages in the L2 norm for functions from the Gordin space is simply calculated and is O(1n√). It is also shown that the Gordin space is a dense set of the first Baire category in L2(Ω,F,μ)⊖L2(Ω,Π(T,F),μ), where Π(T,F) is the Pinsker σ-algebra.
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On the theory of spaces of generalized bessel potentials
Статья научная
The purpose of the article is to introduce norms in the space of generalized Bessel potentials based on the weighted Dirichlet integrals. First, we define weighted Dirichlet integral and show that this integral can be represented using multidimensional generalised translation. Next, we demonstrate that this norm does not allow to define function spaces of arbitrary fractional order of smoothness. The potential theory originates from the theory of electrostatic and gravitational potentials and the Laplace, wave, Helmholtz, and Poisson equations. The famous Riesz potentials are known to be realizations of the real negative powers of the Laplace and wave operators. In the meantime, a lot of attention in the potential theory is given to the Bessel potential. Generalization in the article is achieved by considering the Laplace-Bessel operator which is constructed on the basis of the singular Bessel differential operator. The theory of singular differential equations containing the Bessel operator and the theory of the corresponding weighted function spaces belong to those mathematical areas, the theoretical and applied significance of which can hardly be overestimated.
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