The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R) under mild conditions on the synthesizer ψ ∈ L(R), 1 ≤ p < ∞, with R Rd ψ dx = 1. Here ψj,k(x) = |det aj |ψ(ajx−k), and the dilation matrices aj expand, for example aj = 2I . Affine synthesis further maps a discrete mixed Hardy space `(h) onto H(R). Therefore the H-...

We prove that the Shintani zeta function associated to the space of binary cubic forms cannot be written as a finite sum of Euler products. Our proof also extends to several closely related Dirichlet series. This answers a question of Wright [22] in the negative.

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

Let W a be an affine Weyl group. In 1987 Jian Yi Shi gave characterization of the elements w∈W in terms Φ + -tuples (k(w,α)) α∈Φ called vectors. Using these coefficients, formula is provided to compute standard length . this note we express twisted function coefficients.

an operator associated with the wright function is introduced in the open unit disk. differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. in particular, some inequalities for modified bessel functions are also obtained.