Related papers: Asymptotic Harmonic Analysis on the Space of Squar…
We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.
In this paper, spectral Barron spaces are defined in the framework of quantum harmonic analysis. Their fundamental properties are studied. These include, among others, their completeness structure and some continuous embedding results. As…
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…
The fixed energy scattering matrix is defined on a perturbed stratified medium, and for a class of perturbations, its main part is shown to be a Fourier integral operator on the sphere at infinity. This is facilitated by developing a…
The aim of this note is to introduce a compound basis for the space of symmetric functions. Our basis consists of products of Schur functions and $Q$-functions. The basis elements are indexed by the partitions. It is well known that the…
We present the classification of positive harmonic functions on the Heisenberg group in the case of the southwest measure.
We study infinitesimal semi-simple extrinsic symmetric spaces and give a classification in the symplectic case.
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…
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…
In this paper, we derive a general expression for mth powers of symmetric(0,1)-heptadiagonal matrices with n = 3k order,k = 1,2,3,...,n/3).
This research focuses on the possibility of the surjective relation between symmetric potential function and its scattering matrix in 1-dimension. The theory bases on the property of wave function symmetry and boundary conditions. This…
We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to…
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…
We study spherical functions on the space isomorphic to $U(2n)/(U(n)\times U(n))$ over a $p$-adic field; those functional equations with respect to the action of the Weyl group, the location of possible poles and zeros, explicit formulas,…
We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.
We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asymptotic behavior of the solutions in connection with the changes…