Related papers: Harmonic Analysis on Double Coset Spaces

Let G be a locally compact group, H and K be two closed sub-groups of G, and N be the normalizer group of K in G. In this paper, the existence and properties of a rho-function for the triple (K,G,H) and an N-strongly quasi-invariant measure…

Let S be the group of finite permutations of the naturals 1,2,... The subject of the paper is harmonic analysis for the Gelfand pair (G,K), where G stands for the product of two copies of S while K is the diagonal subgroup in G. The…

We show that quasi-minimizers of non-homogeneous energy functionals on metric measure spaces are locally H\"older continuous and satisfy the Harnack inequality. We assume that the spaces are doubling and support a Poincar\'e inequality. The…

We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type $G/K$ can be used for questions of solvability of systems of invariant differential equations in analogy to…

Using the Maslowski and Seidler method, the existence of invariant measure for 2-dimensional stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise is proved in state space $L_x^2\times H^1$, working with the weak…

Following Boalch-Yamakawa and Meinrenken, we consider a certain class of moduli spaces on bordered surfaces from a quasi-Hamiltonian perspective. For a given Lie group $G$, these character varieties parametrize flat $G$-connections on…

We characterize the absolute continuity of convolution products of orbital measures on the classical, irreducible Riemannian symmetric spaces $G/K$ of Cartan type $III$, where $G$ is a non-compact, connected Lie group and $K$ is a compact,…

Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…

Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C…

We consider the family of harmonic measures on a lamination $\mathcal{L}$ of a compact space $X$ by locally symmetric spaces $L$ of noncompact type, i.e. $L\simeq \Gamma_L\backslash G/K$. We establish a natural bijection between these…

We consider a polyharmonic operator $H=(-\Delta)^l+V(\x)$ in dimension two with $l\geq 2$, $l$ being an integer, and a quasi-periodic potential $V(\x)$. We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there…

Suppose V is a finite dimensional, complex vector space, A is a finite set of codimension one subspaces of V, and G is a finite subgroup of the general linear group GL(V) that permutes the hyperplanes in A. In this paper we study invariants…

Let $G$ be a non-compact group, $K$ the compact subgroup fixed by a Cartan involution and assume $G/K$ is an exceptional, symmetric space, one of Cartan type $E,F $ or $G$. We find the minimal integer, $L(G),$ such that any convolution…

Let $G/H$ be a connected, simply connected homogeneous space of a compact Lie group $G$. We study $G$-invariant quasi-Einstein metrics on the cohomogeneity one manifold $G/H\times (0,1)$ imposing the so-called monotypic condition on $G/H$.…

We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…

Geometric quantization on a coset space $G/H$ is considered, intending to recover Mackey's inequivalent quantizations. It is found that the inequivalent quantizations can be obtained by adopting the symplectic 2-form which leads to Wong's…

In this article, we study stochastic partial differential equations with two reflecting walls, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of…

It is known that for every second countable locally compact group G, there exists a proper G-invariant metric which induces the topology of the group. This is no longer true for coset spaces G/H viewed as G-spaces. We study necessary and…