Mathematics

Given a non-zero polynomial $P(x)$, we study Fuchsian differential operators of the form $L=\partial_x^2-u(x)$ such that for all $\lambda\in\mathbb{C}$ the operator $L+\lambda P(x)$ is monodromy free. We prove that all such operators are…

Let $\mathcal{H}(b)$ be the de Branges-Rovnyak space associated to a non-extreme point $b$ of the unit ball of $H^\infty$, and let $\phi=b/a$, where $a$ is the Pythagorean mate of $b$. It is known that, if $f$ is a function holomorphic on a…

We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible…

We give a simple example of a polynomial contraction automorphism of $\mathbb C^d$, $ d\ge 3 $, with unbounded degree growth. Combined with Poincar\'e-Dulac theorem it provides an algebraic automorphism of $\mathbb C^d$, $ d\ge 3 $, which…

In this short note we give a negative answer to the following open question: \emph{Let $X$ be a $\sigma$-compact paratopological group. Does there exist a continuous isomorphism of $X$ onto a topological group $G$?} Specifically, we…

In this paper, we investigate two subclasses of analytic and univalent functions associated with the exponential mapping $\varphi(z)=e^{\alpha z},\qquad 0<\alpha\le1,$ defined via the subordination conditions $\frac{zf'(z)}{f(z)}\prec…

In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates…

We develop a graphical calculus for monoidal categories equipped with twisted pivotal structures, which are a generalization of pivotal structures originating from the study of orientation structures in the context of the Cobordism…

Dobbs proved that the second iterate of almost every line in the complex plane under the exponential function is dense in the plane. In this paper, we prove an analogous result for the second iterate of the Zorich map in $\mathbb{R}^3$.

In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.

Let $\mathcal{H}(\mathbb{D})$ denote the space of analytic functions in the unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$. For $0<p<\infty$ and $f\in\mathcal{H}(\mathbb{D})$, let $M_p^p(r,f)=\int_0^{2\pi}|f(re^{i\theta})|^p…

We develop an ind-Banach framework for revisiting analytification in complex geometry, inspired by Bambozzi-Chiarellotto-Vanni's work on tempered cohomology. We define several ind-Banach rings of overconvergent and holomorphic power series…

We prove that the set of integrable functions on the unit circle for which the analogue of Paley's theorem for $H^1$ fails is residual in $L^1(\mathbb T)$. Moreover, we establish algebraic genericity and spaceability results in several…

We answer a question of Erd\"os, Herzog, and Piranian on the minimal area of polynomial lemniscates when all the zeros of the polynomial are constrained to lie on a compact set K whose logarithmic capacity is strictly larger than 1.

We develop the theory of $\hbar$-vertex algebras, algebraic structures closely related to vertex algebras but with a deformed translation covariance axiom. We establish their structure theory, including analogues of Goddard's Uniqueness…

We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenke. We obtain inequalities for these metrics under…

In this paper, we introduce and study shifted twisted quantum affine algebras which provide a twisted counterpart of the theory of shifted quantum affine algebras. The shifted twisted quantum affine algebra $\U_q^{\mu_+,\mu_-}(\hgs)$ is…

The goal of this note is to show that the left $\chi$-coalgebra, which is an additional structure on one of the coefficients used in the construction of the cyclic operator for the cyclic sets that generalises the twisted nerve of a group…

Two meromorphic functions $f$ and $g$ are said to weakly share a small function $a$ with bi-weight $(n,k)$ if the functions $f-a$ and $g-a$ have the same zeros with multiplicities truncated at level $n+1$, while zeros whose multiplicities…

Two meromorphic functions $f$ and $g$ are said to weakly share a small function $a$ with bi-weight $(n,k)$ if the functions $f-a$ and $g-a$ have the same zeros with multiplicities truncated at level $n+1$, while zeros whose multiplicities…