相关论文: Equivariant Borel liftings in complex analysis and…

Let $\Omega$ be a Polish space with Borel $\sigma$-field $\mathcal{F}$ and countably generated sub $\sigma$-field $\mathcal{G}\subset\mathcal{F}$. Denote by $\mathcal{L}(\mathcal{F})$ the set of all bounded $\mathcal{F}$-upper semianalytic…

In this paper, we introduce an equivariant analog of Weiss calculus of functors for all finite group $\mathrm{G}$. In our theory, Taylor approximations and derivatives are index by finite dimensional $\mathrm{G}$-representations, and…

The main goal of this paper is to develop a concept of approximate differentiability of higher order for subsets of the Euclidean space that allows to characterize higher order rectifiable sets, extending somehow well known facts for…

In this paper, we investigate shared value problems for shifts and higher-order difference operators of meromorphic and entire functions in several complex variables. Using Nevanlinna theory in $\mathbb{C}^n$, we obtain new uniqueness…

The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field…

Lifting theorems are theorems that bound the communication complexity of a composed function $f\circ g^{n}$ in terms of the query complexity of $f$ and the communication complexity of $g$. Such theorems constitute a powerful generalization…

In a recent work, the authors studied various Borel equivalence relations defined on the Polish space ${\rm{SA}}(H)$ of all (not necessarily bounded) self-adjoint operators on a separable infinite-dimensional Hilbert space $H$. In this…

The Hopf algebra of word-quasi-symmetric functions ($\WQSym$), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the…

It is expected that Schanuel's Conjecture contains all ``reasonable" statements that can be made on the values of {\em the exponential function}. In particular it implies the Lindemann-Weierstrass Theorem and the Conjecture on algebraic…

We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the second…

We extend the Becker--Kechris topological realization and change-of-topology theorems for Polish group actions in several directions. For Polish group actions, we prove a single result that implies the original Becker--Kechris theorems, as…

Borel's rank theorem identifies the ranks of algebraic $K$-groups of the ring of integers of a number field with the orders of vanishing of the Dedekind zeta function attached to the field. Following the work of Gross, we establish a…

Recently a new technique in the harmonic analysis on symmetric spaces was suggested based on certain remarkable representations of affine and double affine Hecke algebras in terms of Dunkl and Demazure operators instead of Lie groups and…

In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and…

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…

The space of Fredholm operators of fixed index is stratified by submanifolds according to the dimension of the kernel. Geometric considerations often lead to questions about the intersections of concrete families of elliptic operators with…

We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…

We introduce the notion of an invariantly universal pair (S,E) where S is an analytic quasi-order and E \subseteq S is an analytic equivalence relation. This means that for any analytic quasi-order R there is a Borel set B invariant under E…

In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…

Classic subdifferentials in variational analysis may fail to fully represent the Bregman proximal operator in the absence of convexity. In this paper, we fill this gap by introducing the left and right \emph{Bregman level proximal…