Related papers: The Bounded Spherical Functions on the Cartan moti…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…
Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.
We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…
We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…
The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functional determinants of the scalar Laplacian on regions of the…
We survey some results concerning finite group actions on products of spheres.
Consider the Gelfand pairs $(G_p,K_p):=(M_{p,q} \rtimes U_p,U_p)$ associated with motion groups over the fields $\mathbb F=\mathbb R,\mathbb C,\mathbb H$ with $p\geq q$ and fixed $q$ as well as the inductive limit $p\to\infty$,the Olshanski…
This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$.
We present an explicit construction of cyclic cocycles on Cartan motion groups, which can be viewed as generalizations of orbital integrals. We show that the higher orbital integral on a real reductive group associated with a semisimple…
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
This paper presents necessary, sufficient, and equivalent conditions for the spherical convexity of non-homogeneous quadratic functions. In addition to motivating this study and identifying useful criteria for determining whether such…
Explicit expressions for zonal spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables.
For a domain $D \subset \mathbb C^n$, the relationship between the squeezing function and the Fridman invariants is clarified. Furthermore, localization properties of these functions are obtained. As applications, some known results…
In this paper we prove Cartan theorems A and B for Stein manifolds over certain discrete valuation rings.
In this study, we construct an analog of the Brownian motion on free unitary quantum groups and compute its cutoff profile.
We characterize functions which are growth types of Riemannian manifolds of bounded geometry.
On the one hand, it is well known that the only subquadratic Dehn function of finitely presented groups is the linear one. On the other hand there is a huge class of Dehn functions $d(n)$ with growth at least $n^4$ (essentially all possible…
In this article, we study the fractional spherical maximal function and its lacunary counterpart. We study the necessary and sufficient conditions for $L^p-L^q$ boundedness of both maximal functions. In particular, we prove the restricted…
This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all…
Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group. It is shown that a universal covering of the de Sitter group gives rise to quaternion…