Related papers: Invertibility Threshold for Nevanlinna Quotient Al…

We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the…

Let $\mathcal{A}$ be a quantized ($K$-theoretic) BFN Coulomb branch with $G=\mathbb{C}^*$ and any $N$, that is, $\mathcal{A}$ is a generalized Weyl or $q$-Weyl algebra. Let $M$ be an $\mathcal{A}$-$\overline{\mathcal{A}}$ bimodule. Choosing…

Operator-valued multivariable Bohr type inequalities are obtained for: a class of noncommutative holomorphic functions, generalizing the analytic functions on the open unit disc; the noncommutative disc algebra and the noncommutative…

This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic function, holds. Second, a difference analogue of logarithmic…

Arbitrary connections on a generic Hopf algebra $H$ are studied and shown to extend to connections on tensor fields. On this ground a general definition of metric compatible connection is proposed. This leads to a sufficient criterion for…

We prove a Fatou-type theorem and its converse for certain positive eigenfunctions of the Laplace-Beltrami operator $\mathcal{L}$ on a Harmonic $NA$ group. We show that a positive eigenfunction $u$ of $\mathcal{L}$ with eigenvalue…

Consider a scaled Nevanlinna-Pick interpolation problem and let $\Pi$ be the Blaschke product whose zeros are the nodes of the problem. It is proved that if $\Pi$ belongs to a certain class of inner functions, then the extremal solutions of…

Let $f_1,f_2$ be linearly independent solutions of $f''+Af=0$, where the coefficient $A$ is an analytic function in the open unit disc $\mathbb{D}$ of $\mathbb{C}$. It is shown that many properties of this differential equation can be…

Let $(X,\mathcal{F},\mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $\sigma$-algebra $\mathcal{F}$ is generated by the intervals according to some total order. The main result is that the…

Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful semifinite normal weight $\phi$ and $\mathcal{N}$ be a von Neumann subalgebra of $\mathcal{M}$ such that the restriction of $\phi$ to $\mathcal{N}$ is semifinite and such…

We propose a definition of sampling set for the Nevanlinna class in the disk, i.e. a subset of the disk such that the analogue of the norm of a function in the Nevanlinna class can be recovered only from its values on the subset. We show it…

We provide results of uniqueness for holomorphic functions in the Nevanlinna class bridging those previously obtained by Hayman and Lyubarskii-Seip. Namely, we propose certain classes of hyperbolically separated sequences in the disk, in…

For a two-dimensional canonical system $y'(t)=zJH(t)y(t)$ on some interval $(a,b)$ whose Hamiltonian $H$ is a.e. positive semi-definite and which is regular at $a$ and in the limit point case at $b$, denote by $q_H$ its Weyl coefficient. De…

We give some criteria for the Lie algebra $\mathrm{HH}^1(B)$ to be solvable, where $B$ is a $p$-block of a finite group algebra, in terms of the action of an inertial quotient of $B$ on a defect group of $B$.

Nevanlinna's five-value theorem is well-known as a famous theorem in value distribution theory, which asserts that two non-constant meromorphic functions on $\mathbb C$ are identical if they share five distinct values ignoring…

One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative surfaces, and this paper resolves a significant case of this problem. Specifically, let S denote the 3-dimensional Sklyanin algebra…

The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…

Given a discrete quantum group $H$ with a finite normal quantum subgroup $G$, we show that any positive, possibly unbounded, harmonic function on $H$ with respect to an irreducible invariant random walk is $G$-invariant. This implies that,…

Let $\left(\mathcal{H},\left(.,.\right)\right)$ be a Hilbert space and let $\mathcal{L}\left(\mathcal{H}\right)$ be the linear space of bounded operators in $\mathcal{H}$. In this paper, we deal with $\mathcal{L}(\mathcal{H})$-valued…

We introduce Nevanlinna classes of holomorphic functions associated to a closed set on the boundary of the unit disc in the complex plane and we get Blaschke type theorems relative to these classes by use of several complex variables…