Related papers: Asymptotic Harmonic Analysis on the Space of Squar…
We study square integrable functions on the metaplectic group and functions on the space of unitary symmetric matrices. We relate them using the oscillator representations.
We investigate the space $X$ of unitary hermitian matrices over $\frp$-adic fields through spherical functions. First we consider Cartan decomposition of $X$, and give precise representatives for fields with odd residual characteristic,…
We are interested in the harmonic analysis on $p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space $X$ of unitary hermitian matrices of odd size over a ${\mathfrak p}$-adic field of odd…
We introduce the space $X$ of quaternion hermitian forms of size $n$ on a ${\mathfrak p}$-adic field with odd residual characteristic, and define typical spherical functions $\omega(x;s)$ on $X$ and give their induction formula on sizes by…
In this paper we study the spherical convexity of quadratic functions on spherically convex sets. In particular, conditions characterizing the spherical convexity of quadratic functions on spherical convex sets associated to the positive…
We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one. We prove the existence of the full asymptotic expansions of these spherical integrals and derive the first and the second term in…
In this paper, we introduce a Helmholtz-type decomposition for the space of square integrable, symmetric-matrix-valued functions analogous to the standard Helmholtz decomposition for vector fields. This decomposition provides a better…
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…
We are interested in the harmonic analysis on $p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space $X$ of unitary hermitian matrices of size $m$ over a ${\mathfrak p}$-adic field $k$ and…
In this paper we prove sharp weak type 1 estimates for spherical Fourier multipliers on symmetric spaces of the noncompact type. This complements earlier results of J.-Ph. Anker and A.D. Ionescu.
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We estimate the asymptotics of spherical integrals when the rank of one matrix is finite. We show that it is given in terms of the R-transform of the spectral measure of the full rank matrix and give a new proof of the fact that the…
In this paper, we present the implicit equations for one special class of real-valued spherical harmonics with octahedral symmetry. Based on this representation, we construct the rotationally invariant measure of deviation from the…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy…
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.
We give explicit models for spherical functions on $p$-adic symmetric spaces $X=H\backslash G$ for pairs of $p$-adic groups $(G,H)$ of the form $(\mathrm{U}(2r),\mathrm{U}(r)\times \mathrm{U}(r)),$ $(\mathrm{O}(2r),\mathrm{O}(r)\times…