Abstract. Solution of some boundary value problems and initial problems in unique ball leads to the convergence and sumability problems of Fourier series of given function by eigenfunctions of Laplace operator on a sphere spherical harmonics. Such a series are called as Fourier-Laplace series on sphere. There are a number of works devoted investigation of these expansions in different topologie...

in the present paper we define strongly δn -summable sequences which generalize a-summablesequences and prove such spaces to be complete paranormed spaces under certain conditions, sometopological results have also been discussed.

The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

The main goal of this paper is to estimate the Hölder norm of a fractal version of the Hilbert transform in the Douglis analysis context acting from Hölder spaces of Douglis algebra valued functions defined on h-summable curves.

In this paper we characterize the probability measures, on Rd, with square summable support, in terms of their associated preservation operators and the commutators of the annihilation and creation operators.

We deal with the following fractional generalization of the Laplace equation for rectangular domains x, y ∈ x0, X0 × y0, Y0 ⊂ R × R , which is associated with the Riemann-Liouville fractional derivativesΔu x, y λu x, y ,Δ : D1 α x0 D 1 β y0 , where λ ∈ C, α, β ∈ 0, 1 × 0, 1 . Reducing the left-hand side of this equation to the sum of fractional integrals by x and y, we then use the operational ...

In this paper we extend the scope of three important results in linear theory absolutely summing operators. The first one was obtained by Bu and Kranz [4] it asserts that a continuous operator between Banach spaces takes almost unconditionally summable sequences into Cohen strongly q-summable for any q≥2, whenever its adjoint is p-summing some p≥1. second them states operators with hilbertian d...

Suppose A is an abelian torsion group with a subgroup G such that A/G is countable that is, in other words, A is a torsion countable abelian extension of G. A problem of some group-theoretic interest is that of whether G ∈ K, a class of abelian groups, does imply that A ∈ K. The aim of the present paper is to settle the question for certain kinds of groups, thus extending a classical result due...

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...