Related papers: Siciak-Zahariuta extremal functions and polynomial…

Let T be a positive plurisubharmonic current of bidimension (p,p) and let $\delta>0$. Assume that the Lelong number of T satisfies $\nu(T,a)\geq \delta$ on a dense subset of supp(T) (rectifiable currents satisfy this condition). Then…

The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…

We define an analogue of the Dirac operator for the degenerate affine Hecke-Clifford algebra. A main result is to relate the central characters of the degenerate affine Hecke-Clifford algebra with the central characters of the Sergeev…

We obtain results on the existence of complex discs in plurisubharmonically convex hulls of Lagrangian and totally real immersions to Stein manifolds.

We prove that any embedded Maslov index two analytic disc attached to a totally real torus in the complex two-dimensional affine space extends to an analytic filling provided that the torus is contained in a regular level set of a strictly…

We introduce and develop the notion of spherical polyharmonics, which are a natural generalisation of spherical harmonics. In particular we study the theory of zonal polyharmonics, which allows us, analogously to zonal harmonics, to…

We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian…

We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…

We study Fuglede's $p$-module of systems of measures in condensers in Euclidean spaces and on polarizable Carnot groups. We apply and generalize a result by Rodin, which provides an explicit method for finding the extremal function and the…

The connection of orthogonal polynomials on the unit circle (OPUC) to the defocusing Ablowitz-Ladik integrable system involves the definition of a Poisson structure on the space of Verblunsky coefficients. In this paper, we compute the…

In this paper we study those polynomials orthogonal with respect to a particular weight over the union of disjoint intervals first introduced by N.I. Akhiezer, via a reformulation as a matrix factorization or Riemann-Hilbert problem. This…

The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…

We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper…

We show that a complex manifold M in the boundary of a smooth bounded pseudoconvex domain in C^n is an obstruction to compactness of the d-bar-Neumann operator on the domain, provided that at some point of M, the Levi form has the maximal…

We use the notion of Milnor fibres of the germ of a meromorphic function and the method of partial resolutions for a study of topology of a polynomial map at infinity (mainly for calculation of the zeta-function of a monodromy). It gives…

We show that complex geometric features of Teichmuller spaces create explicitly the extremals of generic homogeneous holomorphic functionals on univalent functions. In particular this gives proofs of the well-known Zalcman and Bieberbach…

The notion of block divisibility naturally leads one to introduce unitary cyclotomic polynomials. We formulate some basic properties of unitary cyclotomic polynomials and study how they are connected with cyclotomic, inclusion-exclusion and…

We establish a rigid-analytic analog of the Pila-Wilkie counting theorem, giving sub-polynomial upper bounds for the number of rational points in the transcendental part of a $\mathbb{Q}_p$-analytic set, and the number of rational functions…

We show that a disc functional on a complex manifold has a plurisubharmonic envelope if all its pullbacks by holomorphic submersions from domains of holomorphy in affine space do and it is locally bounded above and upper semicontinuous in a…