Related papers: On function spaces on symmetric spaces

Let $L$ be the distinguished Laplacian on the Iwasawa $AN$ group associated with a semisimple Lie group $G$. Assume $F$ is a Borel function on $\mathbb{R}^+$. We give a condition on $F$ such that the kernels of the functions $F(L)$ are…

Let $G$ be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over $\R$. Let $\sigma$ be an involution of the…

Let $Y=\Gamma\backslash H^n$ be a quotient of the hyperbolic space by the action of a discrete convex-cocompact group of isometries. We describe certain spaces of $\Gamma$-invariant currents on the sphere at infinity of $H^n$ with support…

We prove that if $\Sigma$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation…

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…

Hopf algebras, most generally in a semisimple abelian symmetric monoidal category, are here supposed to be commutative but not to be of finite-type, and their (equivariant) smoothness are discussed. Given a Hopf algebra $H$ in a category…

Assume that $p\in[1,\infty]$ and $u=P_{h}[\phi]$, where $\phi\in L^{p}(\mathbb{S}^{n-1},\mathbb{R}^n)$ and $u(0) = 0$. Then we obtain the sharp inequality $|u(x)|\le G_p(|x|)\|\phi\|_{L^{p}}$ for some smooth function $G_p$ vanishing at $0$.…

Let $H$ be a Hilbert space of entire functions. Let $H'$ be the space of the functions $f(z)/\prod_i(z-z_i)$ where $f$ belongs to $H$ and vanishes at $n$ given complex points $z_i$. We compute a suitable $E$ function for $H'$ when one is…

This paper establishes two things in an asymptotically (anti-)de Sitter spacetime, by direct computations in the physical spacetime (i.e. with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is…

We address some global solvability issues for classes of smooth nonsingular vector fields $L$ in the plane related to cohomological equations $Lu=f$ in geometry and dynamical systems. The first main result is that $L$ is not surjective in…

We study the space $S(X)^I$ of smooth functions on a symmetric space $X=G/H$ invariant to the action of an Iwahori subgroup $I$, as a module over $\mathcal{H}(G,I)$, the Iwahori Hecke algebra of a p-adic group $G$. We present a description…

Let $(X, \mathscr{L}, \lambda)$ and $(Y, \mathscr{M}, \mu)$ be finite measure spaces for which there exist $A \in \mathscr{L}$ and $B \in \mathscr{M}$ with either $0 < \lambda(A) < 1 < \lambda(X)$ and $0 < \mu(B) < \mu(Y)$, or the other way…

Let $G$ be a real linear reductive group and let $H$ be a unimodular, locally algebraic subgroup. Let $\operatorname{supp} L^2(G/H)$ be the set of irreducible unitary representations of $G$ contributing to the decomposition of $L^2(G/H)$,…

We obtain sequence space representations for a class of Fr\'echet spaces of entire functions with rapid decay on horizontal strips. In particular, we show that the projective Gelfand-Shilov spaces $\Sigma^1_\nu$ and $\Sigma^\nu_1$ are…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

Let $B^p_{\sigma}$, $1\le p<\infty$, $\sigma>0$, denote the space of all $f\in L^p(\mathbb{R})$ such that the Fourier transform of $f$ (in the sense of distributions) vanishes outside $[-\sigma,\sigma]$. The classical sampling theorem…

In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…

We consider compactifications of the space of triples of distinct points in projective $n$-space. One such space is a singular variety of configurations of points and lines; another is the smooth compactification of Fulton and MacPherson;…

We study umbilically synchronized space-times $M$ that have vanishing electric part of the Weyl tensor and show that (i) If $dim(M) = 4$, then $M$ is conformally flat, (ii) If $dim(M) > 4$, $M$ is conformally flat if and only if the spatial…

We prove that certain means of the quadratical partial sums of the two-dimensional Vilenkin-Fourier series are uniformly bounded operators from the Hardy space $H_{p}$ to the space $L_{p}$ for $0<p\leq 1.$ We also prove that the sequence in…