Related papers: The Bounded Spherical Functions on the Cartan moti…
We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p<1$. We also obtain counterexamples that are asymptotically optimal with our positive…
We introduce the notion of Gelfand pairs and zonal spherical functions for Iwahori-Hecke algebras.
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space $E_n$ are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a…
The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
By considering a spatial curve in a Euclidean space, we use its components, together with attaining a cyclic matrix, to show that this matrix is homothetic too and is in correspondence with a homothetic motion. Furthermore, if the curve…
Bifractional transformations which lead to quantities that interpolate between other known quantities, are considered. They do not form a group, and groupoids are used to described their mathematical structure. Bifractional coherent states…
We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs.…
Using known mode properties, the functional determinant for massless spin-half fields on the Euclidean 4-ball is calculated and shown to be different for spectral (nonlocal) and mixed (local) boundary conditions. The local result agrees…
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
We introduce and study the notion of continuous orbit equivalence of actions of countable discrete groups on Cartan pairs in (twisted) groupoid context. We characterize orbit equivalence of actions in terms of the corresponding…
In this paper we introduce certain analytic functions of boundary rotation bounded by $k\pi$ which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk $E=\{z\in \mathbb{C}\colon…
The rotation group is formulated based on the abstract $B(X)$-module framework. Although the infinitesimal generators of rotation group include differential operators, the rotation group is formulated utilizing the framework of bounded…
We investigate several boundedness properties of function spaces considered as uniform spaces.
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.
In the present paper, we define Morse-Bott functions on manifolds with boundary which are generalizations of Morse functions and show Morse-Bott inequalities for these manifolds.
In the paper, some lower bounds for polygamma functions are refined.
We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…
Sufficient boundary asymptotic conditions are established for a generalized Schur function $f$ to be identically equal to a given rational function $g$ unimodular on the unit circle. Similar rigidity statements are presented for generalized…