Related papers: Singularity barriers and Borel plane analytic prop…

This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption…

We establish Borel equivariant analogues of several classical theorems from complex analysis and PDE. The starting point is an equivariant Weierstrass theorem for entire functions: there exists a Borel mapping which assigns to each…

A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…

We consider a quartic O(N)-vector model. Using the Loop Vertex Expansion, we prove the Borel summability in 1/N along the real axis of the partition function and of the connected correlations of the model. The Borel summability holds…

We prove that the formal $\hbar$-power series solution of the deformed Painlev\'{e} I equation is resurgent, which means it is generically Borel summable and its Borel transform admits endless analytic continuation. In particular, we find…

In this paper we will show that monomial summability can be characterized using Borel-Laplace like integral transformations depending of a parameter $0<s<1$. We will apply this result to prove 1-summability in a monomial of formal solutions…

Let $K\subset R^n$ be a compact basic semi-algebraic set. We provide a necessary and sufficient condition (with no a priori bounding parameter) for a real sequence $y=(y_\alpha)$, $\alpha\in N^n$, to have a finite representing Borel measure…

We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasi-periodic analytic forcing term and in the presence of damping. As a physical application one can think of a…

A class of transformations of $R_q$-matrices is introduced such that the $q\to 1$ limit gives explicit nonstandard $R_{h}$-matrices. The transformation matrix is singular itself at $q\to 1$ limit. For the transformed matrix, the…

The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver and Harrington-Kechris-Louveau show that with respect to Borel reducibility, any…

We address some fundamental problems concerning the structure of idealistic equivalence relations. In particular, we show that, under analytic determinacy, there are continuum many idealistic analytic equivalence relations that are not…

Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…

We investigate a class of elliptic free boundary problems, including a generalized Prandtl Batchelor type problem with a singularity on a stratified Lie group. The associated energy functional is nondifferentiable, which precludes the…

We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of…

We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on…

We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective…

We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract…

This paper develops semiparametric theory for counterfactual distribution, quantile, and lower-tail risk processes under unmeasured confounding using proximal negative-control proxies. Rather than treating each threshold as a separate…

Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to…

We generalize the notion of analytic/Borel equivalence relations, orbit equivalence relations, and Borel reductions between them to their continuous and quantitative counterparts: analytic/Borel pseudometrics, orbit pseudometrics, and Borel…