Related papers: Injectivity in higher order complex domains
We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.
We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are…
A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…
This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map…
We establish that any finite extension of function fields of genus greater than 1 whose relative class group is trivial is Galois and cyclic. This depends on a result from a preceding paper which establishes a finite list of possible Weil…
We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…
In the paper, we first classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,z), h(x,y))$ in the case that $JH$ is nilpotent and $\deg_zv\leq 1$. After that, we generalize the structure of $H$ to…
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
Given a convergent sequence of nodes we present a one-dimensional-holomorphic-function version of the Newton interpolation method of polynomials. It also generalises the Taylor and the Laurent formula. In other words, we present an…
In this paper we are interested in developments of elliptic functions of Jacobi. In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, Editors: C.R.M.…
We estimate the growth of the canonical integral of Hadamard-Weierstrass of measure of finite order on the complex plane by the type of counting function or average counting function of this measure
The Jacobi identities play an important role in constructing the explicit exact solutions of a broad class of integrable systems in soliton theory. In the paper, a direct and simple proof of the Jacobi identities for determinants is…
We derive the Lagrangians of the higher-order Painlev\'e equations using Jacobi's last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painlev\'e test and…
We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, especially in the background of spontaneous compactification. We find that the special extension of Einstein-Maxwell theory with…
We use the Jacobi theta function to give a representation of the modulus of the Riemann $\xi$ function. Based on this modulus representation, we show that the Riemann hypothesis is equivalent to the validity of a family of polynomial…
The Jacobi set is a useful descriptor of mutual behavior of functions defined on a common domain. We introduce the piecewise linear Jacobi set for general vector fields on simplicial complexes. This definition generalizes the definition of…
In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of…
We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in…