Related papers: Weyl-Heisenberg frames for subspaces of L^2(R)

Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the…

This paper establishes Paley-Wiener perturbation theorems for probabilistic frames. The classical Paley-Wiener perturbation theorem shows that if a sequence is close to a basis in a Banach space, then this sequence is also a basis. Similar…

Let $\ggg:=\gl_{m|n}$ be a general linear Lie superalgebra over an algebraically closed field $\mathds{k}=\overline{\mathbb{F}}_p$ of characteristic $p>2$. A module of $\ggg$ is said to be of Kac-Weisfeiler if its dimension coincides with…

Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. In this article we discuss the construction of frames for $L^2(\R^n)$ using the action of closed subgroups $H\subset…

Reductions of N-wave type equations related to simple Lie algebras and the hierarchy of their Hamiltonian structures are studied. The reduction group G_R is realized as a subgroup of the Weyl group of the corresponding algebra. Some of the…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

We study the approximation of functions that map a Euclidean domain $\Omega\subset \mathbb{R}^{d}$ into an $n$-dimensional Riemannian manifold $(M,g)$ minimizing an elliptic, semilinear energy in a function set $H\subset W^{1,2}(\Omega,M)$.…

Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…

We investigate the representations of the hyperalgebras associated to the map algebras $\mathfrak g\otimes \mathcal A$, where $\mathfrak g$ is any finite-dimensional complex simple Lie algebra and $\mathcal A$ is any associative commutative…

The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain…

Let $\Op_t(a)$, for $t\in \mathbf R$, be the pseudo-differential operator $$ f(x) \mapsto (2\pi)^{-n}\iint a((1-t)x+ty,\xi)f(y)e^{i\scal {x-y}\xi} dyd\xi $$ and let $\mathscr I_p$ be the set of Schatten-von Neumann operators of order $p\in…

Restricted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 2. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an…

Let G be a complex semisimple Lie group and H a complex closed connected subgroup. Let g and h be their Lie algebras. We prove that the regular representation of G in $L^2(G/H)$ is tempered if and only if the orthogonal of h in g contains…

We give sufficient and necessary conditions on the Lebesgue exponents for the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restriction to $N=2$ of a result valid for the $N$-fold Weyl…

The first purpose of this article is to provide conditions for a bounded operator in $L^2(\R^n)$ to be the Weyl (resp. anti-Wick) quantization of a bounded continuous symbol on $\R^{2n}$. Then, explicit formulas for the Weyl (resp.…

One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…

Let $\Omega\subset\mathbb{C}^n$ be a domain and $1 \leq q \leq n-1$ fixed. Our purpose in this article is to establish a general sufficient condition for the closed range of the Cauchy-Riemann operator $\bar\partial$ in appropriately…

We identify a class of continuous compactly supported functions for which the known part of the Gabor frame set can be extended. At least for functions with support on an interval of length two, the curve determining the set touches the…

We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The…

Based on the shearlet transform we present a general construction of continuous tight frames for $L^2(\mathbb{R}^2)$ from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems,…