Related papers: Coorbit spaces associated to integrably admissible…

Let $G$ be a reductive group and $\theta$ an involution on $G$, both defined over a $p$-adic field. We provide a criterion for $G^\theta$-integrability of matrix coefficients of representations of $G$ in terms of their exponents along…

We provide explicit criteria for wavelets to give rise to frames and atomic decompositions in ${\rm L}^2(\mathbb{R}^d)$, but also in more general Banach function spaces. We consider wavelet systems that arise by translating and dilating the…

We describe a class of integrable systems on Poisson submanifolds of the affine Poisson-Lie groups $\widehat{PGL}(N)$, which can be enumerated by cyclically irreducible elements the co-extended affine Weyl groups $(\widehat{W}\times…

We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…

We develop a theory of large scale geometry of metrisable topological groups that, in a significant number of cases, allows one to define and identify a unique quasi-isometry type intrinsic to the topological group. Moreover, this…

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Gr\"ochenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of…

In this paper we construct frames of Gabor type for the space $L^2_{rad}(\R^d)$ of radial $L^2$-functions, and more generally, for subspaces of modulation spaces consisting of radial distributions. Hereby, each frame element itself is a…

In this paper we investigate the Besov spaces on compact Lie groups in a subelliptic setting, that is, associated with a family of vector fields, satisfying the H\"ormander condition, and their corresponding sub-Laplacian. Embedding…

Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…

In this paper fundamental nonlinear geometries of Lebesgue sequence spaces are studied in their quantitative aspects. Applications of this work are a positive solution to the strong embeddability problem from $\ell_q$ into $\ell_p$…

Extended admissible groups belong to a particular class of graphs of groups that admit a decomposition generalizing those of non-geometric 3-manifold groups and Croke-Kleiner admissible groups. In this paper, we study several…

This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalised weakly differentiable functions and share key functional…

All four dimensional orbit spaces of compact coregular linear groups have been determined. The results are obtained through the integration of a universal differential equation, that only requires as input the number of elements of an…

Introduced by A. Volberg, matrix $A_{p,\infty}$ weights provide a suitable generalization of Muckenhoupt $A_\infty$ weights from the classical theory. In our previous work, we established new characterizations of these weights. Here, we use…

In this paper, we discuss the embeddability of subspaces of the Gromov-Hausdorff space, which consists of isometry classes of compact metric spaces endowed with the Gromov-Hausdorff distance, into Hilbert spaces. These embeddings are…

Including the previously untreated borderline cases, the trace spaces in the distributional sense of the Besov--Lizorkin--Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the…

We obtain Gabor frame characterisations of modulation spaces defined via a class of translation-modulation invariant Banach spaces of distributions that was recently introduced in $[10]$. We show that these spaces admit an atomic…

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…

The aim of this paper is to study properties of Besov-type spaces with variable smoothness. We show that these spaces are characterized by the phi-transforms in appropriate sequence spaces and we obtain atomic decompositions for these…

We consider a class of semidirect products $G = \mathbb{R}^n \rtimes H$, with $H$ a suitably chosen abelian matrix group. The choice of $H$ ensures that there is a wavelet inversion formula, and we are looking for criteria to decide under…