Related papers: Zero (sub)sets for spaces of holomorphic functions…
In a recent paper [1], it has been shown that negative norm states are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content…
In this article, we introduce a general approach for deriving zero-free half-planes for the Riemann zeta function $\zeta$ by identifying topological vector spaces of analytic functions with specific properties. This approach is applied to…
In a setting, where only "exit measures" are given, as they are associated with an arbitrary right continuous strong Markov process on a separable metric space, we provide simple criteria for the validity of Harnack inequalities for…
We study the problem of classifying the holomorphic $(m,n)$-subharmonic morphisms in complex space. This determines which holomorphic mappings preserves $m$-subharmonicity in the sense that the composition of the holomorphic mapping with a…
Some zero-free regions were known on the right half of the complex plane in the form of vertical strips for fractional hypergeometric zeta functions. In this paper, we describe and demonstrate zero free regions on the left half of the…
We present examples of holomorphic functions that vanish to in- finite order at points at the boundary of their domain of definition. They give rise to examples of Dirichlet minimizing Q-valued functions indicating that "higher"-regularity…
Let $1\leq m\leq n$ be two fixed integers. Let $\Omega \Subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and $\mathcal A \subset \Omega \times ]0,+ \infty[$ a finite set of weighted poles. We define and study properties of the…
The zero sets of harmonic polynomials play a crucial role in the study of the free boundary regularity problem for harmonic measure. In order to understand the fine structure of these free boundaries a detailed study of the singular points…
In this paper, we study the zero sets of the confluent hypergeometric function $_{1}F_{1}(\alpha;\gamma;z):=\sum_{n=0}^{\infty}\frac{(\alpha)_{n}}{n!(\gamma)_{n}}z^{n}$, where $\alpha, \gamma, \gamma-\alpha\not\in \mathbb{Z}_{\leq 0}$, and…
This paper studies loss functions for finite sets. For a given finite set $S$, we give sum-of-square type loss functions of minimum degree. When $S$ is the vertex set of a standard simplex, we show such loss functions have no spurious…
The purpose of this paper is to characterize the zero sets of holomorphic functions in the Nevanlinna class on a class of convex domains of infinite type in $\mathbb{C}^2$. Moreover, we also obtain $L^p$ estimates, $1 \leq p \leq \infty$,…
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…
Among all two-dimensional commutative algebras of the second rank a totally of all their biharmonic bases $\{e_1,e_2\}$, satisfying conditions $\left(e_1^2+ e_2^2\right)^{2} = 0$, $e_1^2 + e_2^2 \ne 0$, is found in an explicit form. A set…
We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…
Let $M$ be a subharmonic function on a domain $D$ in the complex plane $\mathbb C$ with the Riesz measure $\nu_M$. Let $f$ be a non-zero holomorphic function on $D$ such that $\log |f|\leq M$ on $D$ and the function $f$ vanish on a sequence…
Given an o-minimal structure expanding the field of reals, we show a piecewise Weierstrass preparation theorem and a piecewise Weierstrass division theorem for definable holomorphic functions. In the semialgebraic setting and for the…
We consider weighted harmonic Bergman spaces on upper half-space with weights depending only on the vertical coordinate. In these settings, we give full asymptotic expansion of weighted harmonic Bergman kernel as well as full asymptotic…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
We give a condition under which a divisor X in a bounded convex domain of finite type D in C^n is the zero set of a function in a Hardy space H^p(D) for some p \textgreater{} 0. This generalizes Varopoulos' result [Zero sets of H^p…
A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in…