On the global operator and Fueter mapping theorem for slice polyanalytic functions

In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investigate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.

Gateway

Dubai has evolved from fishing village into a transportation and logistics world hub with the largest man-made harbor in the world. From the Dubai base, DP World – as the overall operating company is now known – encompasses a total of 77 marine and inland terminals across the world. As a global operator, DP World now is third in world ranking for container throughput. Under the Dubai regimen, ports push inland to organize or reorganize urban territory at increasingly distant locations, utilizing rail, highway, and air facilities for intermodal logistics systems. The deliberate instituting of multi-modality thus goes beyond the limited physical infrastructure of what is needed for shipping per se and includes free trade zones and other distinctive governance arrangements. Hardware and software aligns to coordinate across global sites. DP World represents success in fostering UAE diversification away from oil and gas and reaching far beyond its borders.

Cuspidality in higher genus

We define a global linear operator that projects holomorphic modular forms defined on the Siegel upper half space of genus [Formula: see text] to all the rational boundaries of lower degrees. This global operator reduces to Siegel's [Formula: see text] operator when considering only the maximal standard cusps of degree [Formula: see text]. One advantage of this generalization is that it allows us to give a general notion of cusp forms in genus [Formula: see text] and to bridge this new notion with the classical one found in the literature.