Related papers: A few remarks concerning complex-analytic metric s…
We discuss local polynomial convexity of real analytic Levi-flat hypersurfaces in $\mathbb C^n$, $n>1$, near singular points.
We give an example of a computably enumerable closed subset of [0,1] that is not homeomorphic to any computably compact space. This answers a question of Koh, Melnikov and Ng.
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
Answering a question raised by V. V. Tkachuk, we present several examples of $\sigma$-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In…
The usual examples of Bergman spaces consist of the closure of an algebra of holomorphic functions on a domain. One can also take the real part of such functions, but essentially one is looking at the same object. In this paper the author…
These informal notes deal with some topics related to analysis on metric spaces.
These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.
We show that several classes of sets, like N_0-sets, Arbault sets, N-sets and pseudo-Dirichlet sets are closed under adding sets of small size.
We classify the metric spaces that can be approximated by finite homogeneous ones.
New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.
A set $X \subseteq 2^\omega$ with positive measure contains a perfect subset. We study such perfect subsets from the viewpoint of computability and prove that these sets can have weak computational strength. Then we connect the existence of…
We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact…
We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…
The aim of this note is to show that every subset of a given topological space is the intersection of a preopen and a preclosed set, therefore $\beta$-locally closed, and that every topological space is $\beta$-submaximal.
We consider inductive limits of weighted spaces of holomorphic functions in the unit ball of $\mathbb C^n$. The relationship between sets of uniqueness, weakly sufficient sets and sampling sets in these spaces is studied. In particular, the…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
Given an n-tuple of multiplication operators on the Bergman space of a bounded pseudoconvex domain in C^n, we study the algebra of their commutants. In particular, we give a geometric description of the maximal C*-subalgebra of this…