Volume 4, Issue 2

Erratum to http://dx.doi.org/10.1515/apam-2012-0025

Abstract. In this article, we give an explicit formula for the Dunkl kernel associated with a positive subsystem of orthogonal roots. We then prove a product formula for this kernel which allows us to show that the Dunkl translation is a bounded operator in this setting. We finally study the Dunkl maximal operator for such subsystems.

Abstract. In this paper, we study properties of the linear functional u satisfying where v is a regular linear functional. We give a necessary and sufficient condition for the regularity of the linear functional u . The coefficients of the three-term recurrence relation, satisfied by the corresponding sequence of orthogonal polynomials, are given explicitly. A study of the semi-classical character of the founded families is done. We conclude with an illustrative example.

Abstract. In this paper, using an abstract linking argument due to Brézis and Nirenberg, we prove a multiplicity result for a class of p ( x )-Kirchhoff problems with Neumann boundary conditions.

Abstract. In [Adv. Pure Appl. Math. 3 (2012), 351–359], we proved a general theorem dealing with summability factors of infinite series by using a quasi-σ-power increasing sequence for some σ . In this paper, we prove that result under less and weaker conditions. Some new and known results are also obtained.

Abstract. In the present paper, the regularity of a Fractal Interpolation Function (FIF) is studied using wavelet transform. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation which FIF satisfies. By this method, it is shown that the FIF belongs to Lipschitz class of order , , under certain conditions on free parameters used in the construction of FIF. The second method is via Fourier transform of FIF. This approach gives the regularity of the FIF under certain conditions on free parameters. The Fourier transform of a FIF is also derived in this paper to facilitate the approach of wavelet transform of a FIF via Fourier transform.

Abstract. A subgroup H of a finite group G is said to be weakly s -semipermutable in G if there exist a subnormal subgroup K of G and an s -semipermutable subgroup of G contained in H such that and . In this paper, we research the influence of weakly s -semipermutability of some primary subgroups on the structure of finite groups. Some new results on p -supersolvability and p -nilpotency of finite groups are shown.

Abstract. If is a projective non-degenerate variety, the X -rank of a point is defined to be the minimum integer r such that P belongs to the span of r points of X . We describe the complete stratification of the fourth secant variety of any Veronese variety  X via the X -rank. This result has an equivalent translation in terms either of symmetric tensors or of homogeneous polynomials. It allows to classify all the possible integers r that can occur in the minimal decomposition of a homogeneous polynomial of X -border rank  (i.e. contained in the fourth secant variety) as a linear combination of powers of linear forms.