Related papers: Injectivity in higher order complex domains

One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.

The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of all bivariate polynomials that…

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…

The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…

In this paper we represent harmonic moments in the language of transfinite functions, that is projective limits of polynomials in infinitely many variables. We obtain also an explicit formula for the Jacobian of a generalized harmonic…

In this paper, we study the approximation of negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in Euclidean domains.

In this paper, we study higher derivations of Jacobian type in positive characteristic. We give a necessary and sufficient condition for $(n-1)$-tuples of polynomials to be extendable in the polynomial ring in $n$ variables over an integral…

We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.

In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.

We derive a new representation for the Weyl function associated with the complex Jacobi matrix in the finite and semi-infinite cases. In our approach we exploit connections to the discrete-time dynamical system associated with these…

Using the Galois theory over function field, and the holomorphy of algebroids defined via irreducible polynomial at singular points, we prove the injectivity of any kellerian mapping. The famous Jacobian conjecture is true.

The purpose of this paper is to introduce into consideration an analogue of the concentration index in the class of subharmonic functions of infinite order. The one in the case of finite order is used in the interpolation theory.

In this paper we solve the Dirichlet problems for different classes of plurisubharmonic functions on compact sets in $\mathbb C^n$ including continuous, pluriharmonic and maximal functions.

We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a…

We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.

We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order…

We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a…