Related papers: Direction problems in affine spaces
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
We discuss solutions of several questions concerning the geometry of conformal planes.
These lecture notes provide an introduction to the theory of Wishart distributions and Wishart processes, particularly what concerns their existence and their realizations as solutions of Wishart SDEs. The material is based on recent…
We study a matrix analog of the Erd\H{o}s-Falconer distance problems in vector spaces over finite fields. There arises an interesting analysis of certain quadratic matrix Gauss sums.
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
We discuss an elementary, yet unsolved, problem of Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields. A short and self-contained account of some recent progress on this…
This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…
This is a review with examples concerning the concepts of affine (in particular, constant and linear) vector fields and fundamental vector fields on a manifold. The affine, linear and constant vector fields on a manifold are shown to be in…
In this paper we investigate complex dynamics in infinite dimensions.
In this survey article we discuss about possible generalizations of Anosov representations in the affine setting and their consequences.
The goal of this article is to investigate infinite dimensional affine diffusion processes on the canonical state space. This includes a derivation of the corresponding system of Riccati differential equations and an existence proof for…
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity…
We find the complete rational homology for the finite subset spaces of a $d$-dimensional sphere. We also determine the integral homology in top $d$ degrees and obtain a partial description of it in codimension $d$.
The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
This expository paper is concerned with the properties of proper holomorphic mappings between domains in complex affine spaces. We discuss some of the main geometric methods of this theory, such as the Reflection Principle, the scaling…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
In this paper, we propose a new method for the construction of multi-dimensional, wavelet-like families of affine frames, commonly referred to as framelets, with specific directional characteristics, small and compact support in space,…
The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.
In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.
In this paper we present a survey on recent developments in the study of ambit fields and point out some open problems. Ambit fields is a class of spatio-temporal stochastic processes, which by its general structure constitutes a flexible…