相关论文: Un theoreme de Kurosh pour les relations d'equival…

We define and study expansion problems on countable structures in the setting of descriptive combinatorics. We consider both expansions on countable Borel equivalence relations and on countable groups, in the Borel, measure and category…

We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a…

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the…

We formulate and prove an analogue of Beurling's theorem for the Fourier transform on the Heisenberg group. As a consequence we deduce Hardy and Cowling-Price theorems.

The concepts of a conditional set, a conditional inclusion relation and a conditional Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in order to construct a conditional topology, a conditional…

In this paper we complete the attempt of H. Lefmann to show that Borel equivalence relations on the $n$-element subsets of $2^{\omega}$, that respect an order type, have a finite Ramsey basis.

We show that every countable Borel equivalence relation structurable by $n$-dimensional contractible simplicial complexes embeds into one which is structurable by such complexes with the further property that each vertex belongs to at most…

We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness.…

By using parallel corona decomposition, the Kerman-Sawyer trace inequality is extended from Lebesgue spaces to product Morrey spaces.

In this paper, we show that, for each $p>1$, there are continuum many Borel equivalence relations between $\Bbb R^\omega/\ell_1$ and $\Bbb R^\omega/\ell_p$ ordered by $\le_B$ which are pairwise Borel incomparable.

We study the class of Borel equivalence relations under continuous reducibility. In particular , we characterize when a Borel equivalence relation with countable equivalence classes is $\Sigma$ 0 $\xi$ (or $\Pi$ 0 $\xi$). We characterize…

The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.

An analogue of Gross' logarithmic Sobolev inequality for a class of elements of noncommutative two tori is proved.

In this paper we present a Kakutani type theorem that is equivalent to the Borsuk--Ulam theorem for manifolds.

We prove an interpolation theorem for bounded free holomorphic functions.

We construct the free products of arbitrary digroups, and thus we solve an open problem of Zhuchok.

Following the topic of the book Canonical Ramsey Theory on Polish Spaces by V. Kanovei, M. Sabok and J. Zapletal we study Borel equivalences on Laver trees. Here we prove that equivalence relations Borel reducible to an equivalence relation…

We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over…

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This…

We prove an analog of Gromov--Lawson type relative index theorems for K-homology classes.