Related papers: Perturbations of Weyl-Heisenberg frames
A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down…
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…
In this note, we prove some results related to small perturbations of a frame for a Hilbert space $\mathcal{H}$ in order to have a woven pair for $\mathcal{H}$. Our results complete those known in the literature. In addition we study a…
In this work, we consider some relationships between a closed range operator $T$ and a fusion frame $\mathcal{W}=(W_i,w_i)_{i\in I}$ for a Hilbert space $\mathcal{H}$ that provides that the sequence $(\overline{T(W_i)},v_i)_{i\in I}$ is a…
In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that…
We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such…
In this paper we have generalized and studied the $K$-Weyl-Heisenberg frames, where $K$ is a bounded linear operator on $L^2(\mathbb{R}^d)$. We have obtained necessary and sufficient conditions for acertain system to be a…
We give sufficient conditions for translates and modulates of a function g in L^2(R) to be a frame for its closed linear span. Even in the case where this family spans all of L^2(R), wou conditions are significantly weaker than the previous…
Let $a$, $b$ be two fixed non-zero constants. A measurable set $E\subset \mathbb{R}$ is called a Weyl-Heisenberg frame set for $(a, b)$ if the function $g=\chi_{E}$ generates a Weyl-Heisenberg frame for $L^2(\mathbb{R})$ under modulates by…
The $\alpha$-modulation transform is a time-frequency transform generated by square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. In this paper we prove new conditions that guarantee the…
We consider the stability of Schauder frames and besselian Schauder frames under perturbations. Our results are inspirit close to the results of Heil [18].
Paley-Wiener theorem for frames for Hilbert spaces, Banach frames, Schauder frames and atomic decompositions for Banach spaces are known. In this paper, we derive Paley-Wiener theorem for p-approximate Schauder frames for separable Banach…
In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…
In 1990, Daubechies proved a fundamental identity for Weyl-Heisenberg systems which is now called the Weyl-Heisenberg Frame Identity. WH-Frame Identity: If $g\in W(L^{\infty},L^{1})$, then for all continuous, compactly supported functions f…
Let $a$, $b$ be two fixed positive constants. A function $g\in L^2({\mathbb R})$ is called a \textit{mother Weyl-Heisenberg frame wavelet} for $(a,b)$ if $g$ generates a frame for $L^2({\mathbb R})$ under modulates by $b$ and translates by…
The Weyl algebra (W_{2m}[h]; *) is the algebra generated by u=(u_1,...,u_m,v_1,.....,v_m) over C with the fundamental commutation relation [u_i,v_j]=-ih\delta_{ij}, where h is a positive constant. The Heisenberg algebra (\Cal H_{2m}[nu];*)…
We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of…
In the present paper, we introduce the notion of $E$-$g$-frames for a separable Hilbert spaces $\mathcal H$, where $E$ is an invertible infinite matrix mapping on the Hilbert space $\mathop\oplus\limits_{n=1}^{\infty}\mathcal H_n$. We study…
Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce the invariance of Fr\'echet frames under perturbation. Also we show that for any Fr\'echet spaces, there is a Fr\'echet frame and any element…
This paper is concerned with frame decompositions of $\alpha$-modulation spaces. These spaces can be obtained as coorbit spaces for square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. The theory…