Related papers: Analytic representation of the generalized Pascal …
In this paper, we study the behavior of a sequence of harmonic maps from surfaces with uniformly bounded energy on the generalized neck domain. The generalized neck domain is a union of ghost bubbles and annular neck domains, which connects…
We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic…
We introduced a new algebra of stochastic generalized functions which contains to the space of stochastic distributions G, [25]. As an application, we prove existence and uniqueness of the solution of a stochastic Cauchy problem involving…
We consider symplectic singularities in the sense of A. Beauville as examples of Poisson schemes. Using Poisson methods, we prove that a symplectic singularity admits a finite stratification with smooth symplectic strata. We also prove that…
This paper presents a natural generalisation of Saxl conjecture from a Lie-theoretical perspective, which is verified for the exceptional types. For classical types, progress is made using spin representations, revealing connections to…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
Some notes and observations on analytic functions defined on an annulus
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…
Analytic approximations of functions of Cayley-Dickson variables are investigated. The case of functions of complexified Cayley-Dickson variables is also encompassed. Moreover, extensions of functions of Cayley-Dickson variables are…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
We give a description of the rational representations of the differential Galois group of a Picard-Vessiot extension.
A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.
We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly give.
In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
We introduce two kinds of generalized $s$-convex functions on real linear fractal sets $\mathbb{R}^{\alpha}(0<\alpha<1)$. And similar to the class situation, we also study the properties of these two kinds of generalized $s$-convex…
In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…
We consider a generalisation of a definite integral involving the Bessel function of the first kind. It is shown that this integral can be expressed in terms of the Fox-Wright function ${}_p\Psi_q(z)$ of one variable. Some consequences of…
Extending the work of Freese, we further develop the theory of generalized trigonometric functions. In particular, we study to what extent the notion of polar form for the complex numbers may be generalized to arbitrary associative…