Related papers: Remarks on one-component inner functions

Given a purely contractive matrix-valued analytic function $\Theta$ on the unit disc $\bm{D}$, we study the $\mc{U} (n)$-parameter family of unitary perturbations of the operator $Z_\Theta$ of multiplication by $z$ in the Hilbert space…

Given a Banach space $\mathcal X$, let $x$ be a point in $\text{ball}(\mathcal X)$, the closed unit ball of $\mathcal X$. One says that $x$ is a strongly extreme point of $\text{ball}(\mathcal X)$ if it has the following property: for every…

A Hilbert point in $H^p(\mathbb{T}^d)$, for $d\geq1$ and $1\leq p \leq \infty$, is a nontrivial function $\varphi$ in $H^p(\mathbb{T}^d)$ such that $\| \varphi \|_{H^p(\mathbb{T}^d)} \leq \|\varphi + f\|_{H^p(\mathbb{T}^d)}$ whenever $f$ is…

A radial weight $\omega$ belongs to the class $\widehat{\mathcal{D}}$ if there exists $C=C(\omega)\ge 1$ such that $\int_r^1 \omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$ for all $0\le r<1$. Write $\omega\in\check{\mathcal{D}}$ if…

The paper develops the result of second Thomae theorem in hyperelliptic case. The main formula, called general Thomae formula, provides expressions for values at zero of the lowest non-vanishing derivatives of theta functions with singular…

Let $\Omega$ be a metric space, $A^t$ denote the metric neighborhood of the set $A\subset\Omega$ of the radius $t$; ${\mathfrak O}$ be the lattice of open sets in $\Omega$ with the partial order $\subseteq$ and the order convergence. The…

Let $\zeta(s)$ and $Z(t)$ be the Riemann zeta function and Hardy's function respectively. We show asymptotic formulas for $\int_0^T Z(t)\zeta(1/2+it)dt$ and $\int_0^T Z^2(t) \zeta(1/2+it)dt$. Furthermore we derive an upper bound for…

We describe an algorithm for computing the inner product between a holomorphic modular form and a unary theta function, in order to determine whether the form is orthogonal to unary theta functions without needing a basis of the entire…

We prove existence and uniqueness of a solution of the Dirichlet problem for separately $(\alpha, \beta)$ - harmonic functions on the unit polydisc $\mathbb D^n$ with boundary data in $C(\mathbb T^n)$ using $(\alpha, \beta)$ - Poisson…

We study the local Lipschitz one subsets of a finite dimensional space, that is, sets for which there exists a continuous function whose local Lipschitz derivative is the characteristic function of said set. We give a characterization of a…

Extending classical results of Janson and Peetre (1988) on the Schatten class $S^p$ membership of commutators of Riesz potentials on the Euclidean space, we obtain analogous results for commutators $[b,T]$, where…

Let $O$ be a one-dimensional Cohen-Macaulay local ring having a finite field as a coefficient field. The aim of this work is to extend the explicit computations of the St\"ohr Zeta Function of $O$ for one and two branches to an arbitrary…

The tetrablock is the set $$ \mathcal{E}=\{x \in \mathbb{C}^3: \quad 1-x_1z-x_2w+x_3z w \neq 0 \quad whenever \quad |z|\leq 1, |w|\leq 1\}. $$ The closure of $\mathcal{E}$ is denoted by $\overline{\mathcal{E}}$. A tetra-inner function is an…

We study eigenfunctions of the Laplace--Beltrami operator \(\Delta_X\) in exterior domains \(\Omega\) of rank-one Riemannian symmetric spaces of noncompact type \(X\), a class that includes all hyperbolic spaces. Extending the classical…

We prove a Clarkson-Erd\"os-Schwartz type theorem for the case of a closed sector in the plane. Concretely, we get some sufficient conditions for the incompleteness and minimality of a M\"untz system $E(\Lambda)={z^{\lambda_n}:n=0,1,...}$…

We construct an analytic self-map $\phi$ of the unit disk and an Orlicz function $\Psi$ for which the composition operator of symbol $\phi$ is compact on the Hardy-Orlicz space $H^\Psi$, but not compact on the Bergman-Orlicz space…

In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane called Zen spaces (which include the Hardy spaces and weighted…

The classical theorems of Mittag-Leffler and Weierstrass show that when $\{\lambda_n\}$ is a sequence of distinct points in the open unit disk $\D$, with no accumulation points in $\D$, and $\{w_n\}$ is any sequence of complex numbers,…

A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under…

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^\Psi$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^\Psi$;…