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

Using the \texttt{WeylModules} \textsf{GAP} Package, we compute structural information about certain Weyl modules for type $G_2$ in characteristic $2$. This gives counterexamples to two conjectures stated by S.~Donkin in 1990. It also…

In this article we obtain families of frames for the space B_\omega of functions with band in [-\omega,\omega] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant,…

Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak h$ and Weyl group $W$. We build up a graded map $(\mathcal H\otimes \bigwedge\mathfrak h\otimes \mathfrak h)^W\to (\bigwedge \mathfrak g\otimes \mathfrak…

Let $1\leq p\leq 2$ and let $\Lambda = \{\lambda_n\}_{n\in \mathbb{N}} \subseteq \mathbb{R}$ be an arbitrary subset. We prove that for any $g\in M^p(\mathbb{R})$ with $1\leq p\leq 2$ the system of translates $\{g(x-\lambda_n)\}_{n\in…

We study the existence of proper holomorphic embeddings of bordered Riemann surfaces into the complex plane C^2. Denote by M(R) the moduli space consisting of all equivalence classes of complex structures J on a given smooth oriented…

Let $(\mathfrak{L},\Gamma)$ be an isometric boundary pair associated with a closed symmetric linear relation $T$ in a Krein space $\mathfrak{H}$. Let $M_\Gamma$ be the Weyl family corresponding to $(\mathfrak{L},\Gamma)$. We cope with two…

We show that any $N$-dimensional linear subspace of $L^2(\mathbb{T})$ admits an orthonormal system such that the $L^2$ norm of the square variation operator $V^2$ is as small as possible. When applied to the span of the trigonometric…

Let $N$ be the Heisenberg group. We consider left-invariant multiplicity free subspaces of $L^2(N)$. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a…

Let f be a cusp form for the group SL(3, Z) with Langlands parameter mu and associated L-function L(s, f). If mu is in generic position, i.e. away from the Weyl chamber walls and away from the self-dual forms, we prove the subconvexity…

We consider compact locally symmetric spaces $\Gamma\backslash G/H$ where $G/H$ is a non-compact semisimple symmetric space and $\Gamma$ is a discrete subgroup of $G$. We discuss some features of the joint spectrum of the (commutative)…

Let $K$ be an infinite field of characteristic $p>0$ and let $\lambda, \mu$ be partitions, where $\mu$ has two parts. We find sufficient arithmetic conditions on $p, \lambda, \mu$ for the existence of a nonzero homomorphism $\Delta(\lambda)…

We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic…

A frame is a system of vectors $S$ in Hilbert space $\mathscr{H}$ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to $S$, for all vectors in $\mathscr{H}$; expressed in…

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are…

Let $f_1,f_2$ be holomorphic modular forms of the same weight for a cocompact lattice $\Gamma < \mathrm{PSL}_2(\mathbf{R})$. We estimate the rate of decay of the coefficients in the expansion of $f_1\overline{f_2}$ in a Laplace eigenbasis.…

G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural…

Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures and preferred connections are introduced…

The van der Geer--van der Vlugt curves form a class of Artin--Schreier coverings of the projective line over finite fields. We provide an explicit formula for their $L$-polynomials in characteristic $2$, expressed in terms of characters of…

Let $M\subset\mathbb{R}^3$ be a properly embedded, connected, complete surface with boundary a convex planar curve $C$, satisfying an elliptic equation $H=f(H^2-K)$, where $H$ and $K$ are the mean and the Gauss curvature respectively -…

The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse)…