The type set for some measures on \mathbb{R}^{2n} with n-dimensional support

Let be realhomogeneous functions in ofdegree and let bethe Borel measure on given by

Representability of Analytic Functions in Terms of Their Boundary Values

Suppose that is an arbitrary finite complex Borel measure on the interval is its Poisson integral, and are the conjugate harmonics of , and is the nontangential limiting value of the analytic function as . In this paper, we consider the problem of representing the analytic function in terms of its boundary values .     

On posets with isomorphic interval posets

Let be a partially ordered set, Int the system of all (nonempty) intervals of partially ordered by the set-theoretical inclusion . We are interested in partially ordered sets with Int isomorphic to Int . We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If is a directed partially ordered set, the only with Int isomorphic to Int are corresponding to direct decompositions of ( denotes the dual of . The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11].     

On Hankel Transform and Hankel Convolution of Beurling Type Distributions Having Upper Bounded Support

In this paper we study Beurling type distributions in the Hankel setting. We consider the space of Beurling type distributions on (0, ) having upper bounded support. The Hankel transform and the Hankel convolution are studied on the space . We also establish Paley Wiener type theorems for Hankel transformations of distributions in .     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

A Completion of \mathbb{Z} is a Field

We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields Further, we show that is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.     

A Comparison on the Commutative Neutrix Convolution of Distributions and the Exchange Formula

Let , be ultradistributions in and let and where is a sequence in which converges to the Dirac-delta function . Then the neutrix product is defined on the space of ultradistributions as the neutrix limit of the sequence provided the limit exist in the sense that

Strictly Cyclic Algebra of Operators Acting on Banach Spaces H p(β)

Let be a sequence of positive numbers and 1 p< . We consider the space H ^p() of all power series such that . We investigate strict cyclicity of the weakly closed algebra generated by the operator of multiplication by zacting on H ^p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra . We also give a necessary condition for a composition operator to be bounded on H ^p() when is strictly cyclic.     

Upper Bounds of the Lebesgue Constants for Fourier–Jacobi Series Summation Methods Defined by a Multiplier Function

Let be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators generated by a multiplier matrix defined by the following relations:

Description of Simple Exceptional Sets in the Unit Ball

For z B ⁿ, the boundary of the unit ball in . If the exceptional set for f. In this note we give a tool for describing such sets. Moreover we prove that if Eis a G and F subset of the projective (n– 1)-dimensional space then there exists a holomorphic function fin the unit ball B ⁿso that E(f) = E.     

Commutants and derivation ranges

In this paper we obtain some results concerning the set , where is the closure in the norm topology of the range of the inner derivation _A defined by _A (X) = AX – XA. Here stands for a Hilbert space and we prove that every compact operator in is quasinilpotent if A is dominant, where is the closure of the range of _A in the weak topology.     

On Uniformly Locally Compact Quasi-Uniform Hyperspaces

We characterize those Tychonoff quasi-uniform spaces for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family of nonempty compact subsets of X. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space Xis uniformly locally compact on if and only if Xis paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show that a Hausdorff topological space is -compact if and only if its (lower) semi-continuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on is obtained.     

Light paths with an odd number of vertices in polyhedral maps

Let P _k be a path on k vertices. In an earlier paper we have proved that each polyhedral map G on any compact 2-manifold with Euler characteristic contains a path P _k such that each vertex of this path has, in G, degree . Moreover, this bound is attained for k = 1 or k 2, k even. In this paper we prove that for each odd , this bound is the best possible on infinitely many compact 2-manifolds, but on infinitely many other compact 2-manifolds the upper bound can be lowered to .     

On a Problem Concerning k-Subdomination Numbers of Graphs

One of numerical invariants concerning domination in graphs is the k-subdomination number of a graph G. A conjecture concerning it was expressed by J.H. Hattingh, namely that for any connected graph G with n vertices and any k with the inequality holds. This paper presents a simple counterexample which disproves this conjecture. This counterexample is the graph of the three-dimensional cube and k = 5.     

The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals

We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, , where R is a compact interval of , and f are functions with values on L(Z,W) and Z respectively, and Z and W are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, , as well as to unbounded intervals R.     

Bounded Oscillation of Nonlinear Neutral Differential Equations of Arbitrary Order

The paper is concerned with oscillation properties of n-th order neutral differential equations of the form

Almost periodic compactifications of group extensions

Let and be groups and let be an extension of by . Given a property of group compactifications, one can ask whether there exist compactifications and of N and K such that the universal -compactification of G is canonically isomorphic to an extension of by . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties and then apply this result to the almost periodic and weakly almost periodic compactifications of G.     

On intervals and isometries of MV-algebras

Let Int be the lattice of all intervals of an MV-algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.     

On Topological Classification of Non-Archimedean Fréchet Spaces

We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field is homeomorphic to the non-archimedean Fréchet space .