Related papers: Paley--Wiener theorems on the Siegel upper half-sp…

This article contains a Wiener Lemma for the convolution algebra $\ell^1(\mathbb H,\mathbb C)$ and group $C^\ast$-algebra $C^\ast(\mathbb H)$ of the discrete Heisenberg group $\mathbb H$. At first, a short review of Wiener's Lemma in its…

This article provides a thorough investigation into Gilbert's Conjecture, pertaining to Hardy spaces in the upper half-space valued in Clifford modules. We explore the conjecture proposed by Gilbert in 1991, which seeks to extend the…

Here we give a new approach to the Paley--Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of "polar-analytic function" in the…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method…

In quantum theory on curved backgrounds, Heisenberg's uncertainty principle is usually discussed in terms of ensemble variances and flat-space commutators. Here we take a different, preparation-based viewpoint tailored to sharp position…

The definition of classical holomorphic function spaces such as the Hardy space or the Dirichlet space on the Hartogs triangle is not canonical. In this paper we introduce a natural family of holomorphic function spaces on the Hartogs…

We prove uniform resolvent estimates in weighted $L^2$-spaces for the sublaplacian $\mathcal{L}$ on the Heisenberg group $\mathbb{H}^d$. The proof are based on multiplier methods, and strongly rely on the use of horizontal multipliers and…

We present a natural family of Hilbert function spaces on the d-dimensional complex unit ball and classify which of them satisfy that subsets of the ball yield isometrically isomorphic subspaces if and only if there is an analytic…

We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…

The main focus of the paper is the investigation of moduli space of left invariant pseudoRiemannian metrics on the cotangent bundle of Heisenberg group. Consideration of orbits of the automorphism group naturally acting on the space of the…

Let $G$ be (the rational points of) a connected reductive group over a local non-archimedean field $F$. In this article we formulate and prove a property of an $F$-spherical homogeneous $G$-space (which in addition satisfies the finite…

Let $H := \begin{pmatrix} 1 & {\mathbf R} & {\mathbf R} \\ 0 & 1 &{\mathbf R} \\ 0 & 0 & 1 \end{pmatrix}$ denote the Heisenberg group with the usual Carnot-Carath\'eodory metric $d$. It is known (since the work of Pansu and Semmes) that the…

The images of Hermite and Laguerre Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterised. These are used to characterise the Schwartz class of rapidly decreasing functions. The image of the space…

We use holography to study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory with gauge group SU(Nc), in the large-Nc and large-coupling limits, coupled to a single massless (n+1)-dimensional hypermultiplet in the fundamental…

In this paper, we prove some Paley-Wiener theorems for function spaces consisting of slice monogenic functions such as Paley-Wiener, Hardy and Bergman spaces. As applications, we can compute the reproducing kernel functions for the related…

This paper conducts a geometric analysis of the Joint-Eigenspace Fourier transform of the symmetric space of the non-compact type. Our study shows how the Poisson transform builds up the well-known Helgason Fourier transform for an analysis…

We characterize the Besov spaces associated to the Gelfand pairs on the Heisenberg group. The characterization is given in terms of bandlimited wavelet coefficients where the bandlimitedness is introduced using spherical Fourier transform.…

We study the metric and topological properties of the space $\mathscr{D}(G)$ of left-invariant hyperbolic pseudometrics on the non-elementary hyperbolic group $G$ that are quasi-isometric to a word metric, up to rough similarity. This space…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…