Related papers: Invariant Meromorphic Functions on the Wallpaper G…
Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for…
The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and…
In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action…
n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…
In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup. As our main result we construct quotients of Rosenlicht-type for Stein spaces acted upon holomorphically by complex-reductive Lie…
We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…
We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then…
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under…
Using the locally compact abelian group $\BT \times \BZ$, we assign a meromorphic function to each ideal triangulation of a 3-manifold with torus boundary components. The function is invariant under all 2--3 Pachner moves, and thus is a…
We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of…
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
We provide a framework for the construction of diffeomorphism invariant sheaves of nonlinear generalized functions spaces. As an application, global algebras of generalized functions for distributions on manifolds and diffeomorphism…
In the study of holomorphic functions of one complex variable, one well-known theory is that of elliptic functions and it is possible to take the zeta-function of Weierstrass as a building stone of this vast theory. We are working the…