相关论文: Holomorphic extensions of representations: (II) ge…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
This paper is the second part of arXiv:0707.1766. We develope harmonic analysis in some categories of filtered abelian groups and vector spaces over the fields R or C. These categories contain as objects local fields and adelic spaces…
We classify biharmonic and harmonic homomorphisms $f:(G,g_1)\rightarrow(G,g_2)$ where $G$ is a connected and simply connected three-dimensional unimodular Lie group and $g_1$ and $g_2$ are left invariant Riemannian metrics.
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…
Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
The aim of this paper is two-fold: first, we look at the fractional Laplacian and the conformal fractional Laplacian from the general framework of representation theory on symmetric spaces and, second, we construct new boundary operators…
This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.
In this paper we define and discuss the representations of $n$-BiHom-Lie algebra. We also introduce $T_{\theta}$-extensions and $T_{\theta}^{\ast}$-extensions of $n$-BiHom-Lie algebras and prove the necessary and sufficient conditions for a…
We survey some principal results and open problems related to colorings of geometric and algebraic objects endowed with symmetries, concentrating the exposition on the maximal symmetry numbers of such objects.
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous…
We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.
We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite…
We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.