相关论文: On Harish-Chandra theory of global nonsymmetric fu…

Value of generalized hypergeometric function at a special point is calculated. More precisely, value of certain multiple integral over vanishing cycle (all arguments collapse to unity) is calculated. The answer is expressed in terms of…

In the last ten years a technique of Schur generating functions and Harish-Chandra transforms was developed for the study of the asymptotic behavior of discrete particle systems and random matrices. In the current paper we extend this…

We develop the general theory of Jack-Laurent symmetric functions, which are certain generalisations of the Jack symmetric functions, depending on an additional parameter p_0.

We continue our investigation of Hardy-type inequalities involving combinations of cylindrical and spherical weights. Compared to [Cora-Musina-Nazarov, Ann. Sc. Norm. Sup., 2024], where the quasi-spherical case was considered, we handle the…

We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions. We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from…

Let $L_H$ denote the set of all normalized locally one-to-one and sense-preserving harmonic functions in the unit disc $\Delta$. It is well-known that every complex-valued harmonic function in the unit disc $\Delta$ can be uniquely…

We rewrite Arthur's asymptotic formula for weighted orbital integrals on real groups with the aid of a residue calculus and extend the resulting formula to the Schwartz space. Then we extract the available information about the coefficients…

We give a general expression of spherical functions on $p$-adic homogeneous spaces of $G$, based on data of $G$ and functional equations of spherical functions. Then, we show a unified method to obtain functional equations of spherical…

In this paper, we study some anisotropic singular perturbations for a class of linear elliptic problems. We show a global asymptotic expansion of the solution in certain functional space.

We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under…

In this paper, we introduce the Harish-Chandra homomorphism for the quantum superalgebra $\mathrm{U}_q(\mathfrak{g})$ associated with a simple basic Lie superalgebra $\mathfrak{g}$ and give an explicit description of its image. We use it to…

We will use a discrete analogue of the classical Laplace method to show that for infinitely many positive integers $n$, the main term of the asymptotic expansion of the scaled $q$-exponential $(-q^{-nt+1/2}u;q)_{\infty}$ could be expressed…

We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidence algebra of the lattice of noncrossing…

We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct…

The aim of this article is to give a complete proof of results of Harish-Chandra linking the irreducibility of parabolic induction of a supercuspidal representation of a p-adic group to the analytic behavior of the mu-function of…

This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative…

We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…

We will use a discrete analogue of the classical Laplace method to show that the main term of the asymptotic expansions of certain entire functions, including Ramanujan's entire function $A_{q}(z)$, can be expressed in terms of…

We show that we can approximate every function $f\in C^{k}(\bar{B_1})$ with a $s$-harmonic function in $B_1$ that vanishes outside a compact set. That is, $s$-harmonic functions are dense in $C^{k}_{\rm{loc}}$. This result is clearly in…

The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $\Lambda$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.)…