Related papers: Zero (sub)sets for spaces of holomorphic functions…
We study the limits of pluricomplex Green functions with four poles tending to the origin in a hyperconvex domain, and the (related) limits of the ideals of holomorphic functions vanishing on those points. Taking subsequences, we always…
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…
The Dirichlet--Hardy space $\Ht$ consists of those Dirichlet series $\sum_n a_n n^{-s}$ for which $\sum_n |a_n|^2<\infty$. It is shown that the Blaschke condition in the half-plane $\operatorname{Re} s>1/2$ is a necessary and sufficient…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex $X$ including their connectivity and their top homology groups. It also discusses the inclusion of the…
Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is…
C-holomorphic functions defined on algebraic sets and having algebraic graphs can be considered as a complex counterpart of regulous functions introduced recently in real geometry. This note is a part of our study on the subject; we prove…
We show that there exists a unique possible definition, with certain natural properties, of the multiple point space of a holomorphic map between complex manifolds. Our construction coincides with the double point space and the k-th…
We give an analysis of the spin-weighted Green's functions well-defined in a conical space. We apply these results in the case of a straight cosmic string and in the Rindler space in order to determine generally the Euclidean Green's…
For a group $G$ acting over a set $X$, the set of all the $G$-equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\in G, \forall x\in X$), is a monoid with the composition.…
For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X\times Y,Z)$ we denote the space of all separately continuous functions $f:X\times Y\to Z$ endowed with the topology of layer-wise uniform convergence,…
We consider convergence sets of formal power series of the form $f(z,t)=\sum_{n=0}^{\infty} f_n(z)t^n$, where $f_n(z)$ are holomorphic functions on a domain $\Omega$ in $\mathbb{C}$. A subset $E$ of $\Omega$ is said to be a convergence set…
A smooth, compact 4-manifold with a Riemannian metric and b^(2+) > 0 has a non-trivial, closed, self-dual 2-form. If the metric is generic, then the zero set of this form is a disjoint union of circles. On the complement of this zero set,…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
The main result of this paper shows a totally new necessary and sufficient condition to determine both real and complex zeros of derivative of all entire and meromorphic functions of one complex variable in the extended complex plane. By…
Combinatorial properties of zeons have been applied to graph enumeration problems, graph colorings, routing problems in communication networks, partition-dependent stochastic integrals, and Boolean satisfiability. Power series of elementary…
The (partially) ordered set of the non-trivial zeros of the zeta function with positive imaginary parts is considered. The order is the coordinatewise order inherited from $\mathbb{C}$. Some interesting properties regarding the minimal…
We give a formula for the values of automorphic Green functions on the special rational 0-cycles (big CM points) attached to certain maximal tori in the Shimura varieties associated to rational quadratic spaces of signature (2d,2). Our…
Asymptotic formulae for Green's functions for the operator $-\GD$ in domains with small holes are obtained. A new feature of these formulae is their uniformity with respect to the independent variables. The cases of multi-dimensional and…
The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carath\'eodory…