Related papers: Some extremal problems for martingale transforms. …

We study relationships between different formulations of the local principle. Also we establish a connection among the local principle and the non-commutative Fourier transform approach to the investigation of convolution operator algebras.…

Local existence properties of initial boundary value problems associated with a new type of systems of differential equations with "maxima" are investigated.

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…

In this paper we consider Yamabe type problem for higher order curvatures on manifolds with totally geodesic boundaries. We prove local gradient and second derivative estimates for solutions to the fully nonlinear elliptic equations…

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results…

In this paper we introduce a variant of Burkholder's martingale transform associated with two martingales with respect to different filtrations. Even though the classical martingale techniques cannot be applied, we show that the discussed…

We deal with various alternative decompositions of F-martingales with respect to the filtration G which represents the enlargement of a filtration F by a progressive flow of observations of a random time that either belongs to the class of…

We prove the existence of Local Uniformization for rational codimension one foliations along rational rank one valuations, in any ambient dimension. This result is consequence of the Truncated Local Uniformization of integrable formal…

The $r$-fold edgewise subdivision is a well studied flag triangulation of the simplex with interesting algebraic, combinatorial and geometric properties. An important enumerative invariant, namely the local $h$-polynomial, of this…

We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem…

We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…

This paper is an edited and shortened version of Chapter 6 from the thesis of the author. First the one dimensional orthogonal derivative will be extended to the two-dimensional case. In the two-dimensional case we have to define the region…

This is a survey of old and new problems and results in additive number theory.

In this paper we investigate in details derivations on trivial extension algebras. We obtain generalizations of both known results on derivations on triangular matrix algebras and a known result on first cohomology group of trivial…

In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of…

Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an…

The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…

The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…

This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…

A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide…