We propose to associate a modular form (an infinite number of) complex valued functions on the $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. elaborate correspondence and study its consequence in terms of Mellin transforms $L$-functions related forms. Further we discuss case products Dirichlet their duals, which are convolution $\vartheta$-series. The latter intriguingly similar non-holomo...

The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

Kubota [19] showed how the theory of Eisenstein series on the higher metaplectic covers of SL2 (which he discovered) can be used to study the analytic properties of Dirichlet series formed with n-th order Gauss sums. In this paper we will prove a functional equation for such Dirichlet series in the precise form required by the companion paper [2]. Closely related results are in Eckhardt and Pat...

This introductory article aims to provide a roadmap to many of the interrelated papers in this volume and to a portion of the field of multiple Dirichlet series, particularly emerging new ideas. It is both a survey of the recent literature, and an introduction to the combinatorial aspects of Weyl group multiple Dirichlet series, a class of multiple Dirichlet series that are not Euler products, ...

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of Métivier and Pellaumail which is quite restrictive. We make use of the notion of χ-covariation which is a generalized notion of covariation for processes with values in two Banach spaces B1 and B2. χ refers to a suitable subspace of the dual ...

Given a hypergraph H = (V,F) and a [0, 1]-valued vector a ∈ [0, 1] , its global rounding is a binary (i.e.,{0, 1}-valued) vector α ∈ {0, 1} such that | ∑ v∈F (a(v)−α(v))| < 1 holds for each F ∈ F . We study geometric (or combinatorial) structure of the set of global roundings of a using the notion of compatible set with respect to the discrepancy distance. We conjecture that the set of global r...

the paper presents the semi-numerical solution for the magnetohydrodynamic (mhd) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. the governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (node) by using a classical similarity transformation along with appropriate boundary cond...

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...