相关论文: An integral transform connecting spherical analysi…
We define a new integral transform on the real sphere which is invariant relative to the orthogonal group and similar to the horospherical Radon transform for the hyperbolic space. This transform involves complex geometry associated with…
The main purpose of this paper is to compute all irreducible spherical functions on $G={SL}(2,{\mathbb C})$ of arbitrary type $\delta\in \hat K$, where $K={SU}(2)$. This is accomplished by associating to a spherical function $\Phi$ on $G$ a…
Asymptotic expansions as well as necessary and sufficient conditions are provided for the pointwise convergence of the spherical partial integrals of the associated Fourier transforms on the real hyperbolic space. The proposed method…
This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…
We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces $Z=G/H$ attached to a real reductive Lie group $G$. A special emphasis is made to the case where $Z$ is real spherical.
This paper deals with various topics in analysis on hyperbolic spaces. It surveys some recent progress in non-Euclidean Fourier Analysis and proves some new results for the geodesic Radon transform on hyperbolic spaces.
In this work, we investigate new solutions to the decoration transformation in terms of various special functions, including the hyperbolic gamma function, the basic hypergeometric function, and the Euler gamma function. These solutions to…
We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex…
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex…
We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
A non-uniqueness phase for infinite clusters is proven for a class of marked random connection models on the $d$-dimensional hyperbolic space, ${\mathbb{H}^d}$, in a high volume-scaling regime. The approach taken in this paper utilizes the…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
By means of the contour integration method, we evaluate, in closed form, a class of definite integrals involving hyperbolic tangent function.
This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex…
We settle a long standing issue concerning the traditional derivation of non-compact non-linear sigma models in the theory of disordered electron systems: the hyperbolic Hubbard-Stratonovich (HS) transformation of Pruisken-Schaefer type.…
We report on a recent progress in constructing off-shell ${\cal N}=2, 4D$ supersymmetric integer higher-spin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with the matter hypermultiplets.…
By analogy with complex numbers, a system of hyperbolic numbers can be introduced in the same way: z=x+h*y with h*h=1 and x,y real numbers. As complex numbers are linked to the Euclidean geometry, so this system of numbers is linked to the…