Related papers: Dorronsoro's theorem and a small generalization

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

We consider row sequences of vector valued Pad\'{e}-Faber approximants (simultaneous Pad\'{e}-Faber approximants) and prove a Montessus de Ballore type theorem.

We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We give an elementary proof of a generalization of Rokhlin's lemma for commuting non-invertible measure-preserving transformations, and we present several combinatorial applications.

In this paper we first prove that a simple root of a polynomial satisfies the Sendov's conjecture. As the multiple roots trivially satisfy the Sendov's conjecture we conclude that the Sendov's conjecture holds true.

Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.

This paper has two objectives: we first generalize the theory of Abhyankar-Moh to quasi-ordinary polynomials, then we use the notion of approximate roots and that of generalized Newton polygons in order to prove the embedding conjecture for…

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

A p-adic analogue of the pseudonorm version of the birational Torelli type theorem is obtained via a comparison theorem of image closures. Among other results obtained, we have a criterion for existence of rational points of canonically…

We give a purely combinatorial proof for the infinitary van der Waerden's theorem.

We prove a fix point theorem for monoids of self-embeddings of trees. As a corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either contains a subdivided binary tree as a subtree or has a vertex, and edge, an end or…

We extend Edmonds' Branching Theorem to locally finite infinite digraphs. As examples of Oxley or Aharoni and Thomassen show, this cannot be done using ordinary arborescences, whose underlying graphs are trees. Instead we introduce the…

This paper states and proves a generalization of the well-known Desargues involution theorem from plane projective geometry.

We present intersection type systems in the style of sequent calculus, modifying the systems that Valentini introduced to prove normalisation properties without using the reducibility method. Our systems are more natural than Valentini's…

We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition…

We provide a short proof of the 1-dimensional flat chain conjecture.

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of Gallagher's theorem, sharpening and making unconditional a…

We give an alternative definition of integral at the generality of the Perron integral and propose an exposition of the foundations of integral theory starting from this new definition. Both definition and proofs needed for the development…