Related papers: Multi-window Gabor frames in amalgam spaces

The concept of (p,q)-pair frames is generalized to (l,l^*)-pair frames. Adjoint (conjugate) of a pair frames for dual space of a Banach space is introduced and some conditions for the existence of adjoint (conjugate) of pair frames are…

Given discrete subsets $\Lambda_j\subset {\Bbb R}^d$, $j=1,...,q$, consider the set of windowed exponentials $\bigcup_{j=1}^{q}\{g_j(x)e^{2\pi i <\lambda,x>}: \lambda\in\Lambda_j\}$ on $L^2(\Omega)$. We show that a necessary and sufficient…

Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have contributed to the discovery of many other finite-dimensional…

It is shown that all the approximately finite dimensional C*-algebras which are not of Type I are isomorphic as Banach spaces. This generalises the matroid case given previously by Arazy. Analogous results are obtained for various families…

We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\mathbb{Z})$ of $p$-pseudofunctions on $\mathbb{Z}$, the…

We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the…

Let $0<p\leq 1$, $\omega$ be a weight on $\mathbb Z$, and let $\mathcal A$ be a unital Banach algebra. If $f$ is a continuous function from the unit circle $\mathbb T$ to $\mathcal A$ such that $\sum_{n\in \mathbb Z} \|\widehat f(n)\|^p…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

Let $\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty$. Let $\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty$. Define $\acn$ to…

M-branes are related to theories on function spaces $\cal{A}$ involving M-linear non-commutative maps from $\cal{A} \times \cdots \times \cal{A}$ to $\cal{A}$. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of $T^M$…

In this paper we present a rare combination of abstract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sampling problems. We show that for a large class of slanted…

Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…

Let $\mathscr B$ be a normal quasi-Banach function space with respect to $r_0 \in (0,1]$ and $v_0$, $\omega$ be $v$-moderate, and let $r\in [r_0,\infty ]$. Then we prove that $f$ belongs to the modulation space $M(\omega ,\mathscr B )$, iff…

See title. (A Banach space is said to be L-embedded if it is complemented in its bidual such that the norm between the two complementary subspaces is additive.)

In the first part of the paper we describe the dual \ell^2(A)^{\prime} of the standard Hilbert C*-module \ell^2(A) over an arbitrary (not necessarily unital) C*-algebra A. When A is a von Neumann algebra, this enables us to construct…

We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition…

Let $A$ and $B$ be unital Banach algebras with $A$ a subalgebra of $B$. Denote the algebra of all $n\times n$ matrices with entries from $A$ by $M_{n}(A)$. In this paper we prove some results concerning the open question: If $A$ is inverse…

In this work we derive a simple argument which shows that Gabor systems consisting of odd functions of $d$ variables and symplectic lattices of density $2^d$ cannot constitute a Gabor frame. In the 1--dimensional, separable case, this is a…

We investigate the completeness of Gabor systems with respect to several classes of window functions on rational lattices. Our main results show that the time-frequency shifts of every finite linear combination of Hermite functions with…

The main result is that there are infinitely many; in fact, a continuum; of closed ideals in the Banach algebra $L(L_1)$ of bounded linear operators on $L_1(0,1)$. This answers a question from A. Pietsch's 1978 book "Operator Ideals". The…