Related papers: Iterated convolutions and endless Riemann surfaces

We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \mathscr Q(z)}$ depending on a potential $\mathscr Q:\mathbb C^d\to\mathbb R$. We use these kernels to construct determinantal point processes on…

The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional…

Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus,…

The generating series associated to a certain sequence of limited Taylor expansions coincides with the continuously iterated Invert Transform and displays thus a nice functional equality.

In this paper, a construction of an infinite dimensional associative algebra, which will be called a \emph{Surface Algebra}, is associated in a "canonical" way to a dessin d'enfant, or more generally, a cellularly embedded graph in a…

We show that properties of pairs of finite, positive and regular Borel measures on the complex unit circle such as domination, absolute continuity and singularity can be completely described in terms of containment and intersection of their…

In this paper, we show that if $(U_n)_{n\ge 1}$ is any nondegenerate linearly recurrent sequence of integers whose general term is up to sign not a polynomial in $n$, then the inequality $\phi(|U_n|)\ge |U_{\phi(n)}|$ holds on a set of…

A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…

With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…

We prove the following well known conjecture: let $\Sigma$ be an oriented surface of finite type whose fundamental group is a nonabelian free group. Let $\phi \in \textup{Mod}(\Sigma)$ be a an infinite order mapping class. Then there exists…

We introduce the nonlocal analogue of the classical free boundary minimal hypersurfaces in an open domain $\Omega$ of $\mathbb{R}^n$ as the (boundaries of) critical points of the fractional perimeter $\operatorname{Per}_s(\cdot,\,\Omega )$…

In this work, we want to show several properties of an unnodal, complex Coble surface $X$ with irreducible boundary curve $C \in |-2 K_X|$. Namely, we show that every isotropic sequence ${\cal E}_1, \ldots, {\cal E}_r$ with $r \le 8$ and…

Let $ \Omega \subsetneq \mathbf{R}^n\,(n\geq 2)$ be an unbounded convex domain. We study the minimal surface equation in $\Omega$ with boundary value given by the sum of a linear function and a bounded uniformly continuous function in $…

An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…

In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…

In this paper we generalize some constructions and results due to Cayley and Hilbert. We define the concept of $\Omega$--process for an arbitrary algebraic monoid with zero and unit group $G$. Then we show how to produce from the process…

We define ''convergence'' for noncommutative power series and construct two topologies on the algebra of power series, convergent with respect to a positive radius. We indicate all finite dimensional continuous representations of this…

We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is…

Let $C$ be a closed cone with nonempty interior $C^\circ$ in a Banach space. Let $f:C^\circ \rightarrow C^\circ$ be an order-preserving subhomogeneous function with a fixed point in $C^\circ$. We introduce a condition which guarantees that…

This paper is concerned with projective rationally connected surfaces $X$ with canonical singularities and having non-zero pluri-forms, i.e. $(\Omega_X^1)^{[\otimes m]}$ has non-zero global sections for some m > 0, where…