Related papers: A fundamental identity for Parseval frames

In this paper we consider on the notion of continuous frame of subspace and define a new concept of continuous frame, entitled {\it continuous atomic resolution of identity}, for arbitrary Hilbert space $\h$ which has a countable…

Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…

In this paper, we focus on frames of operators or K-frames on Hilbert spaces in Parseval cases. Since equal-norm tight frames play important roles for robust data transmission, we aim to study this topics on Parseval K-frames. We will show…

We give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These…

In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we…

We answer a number of open problems in frame theory concerning the decomposition of frames into linearly independent and/or spanning sets. We prove that in finite dimensional Hilbert spaces, Parseval frames with norms bounded away from 1…

In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…

Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…

Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is…

In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a…

This paper examines the construction and properties of binary Parseval frames. We address two questions: When does a binary Parseval frame have a complementary Parseval frame? Which binary symmetric idempotent matrices are Gram matrices of…

We construct Parseval wavelet frames in $L^2(M)$ for a general Riemannian manifold $M$ and we show the existence of wavelet unconditional frames in $L^p(M)$ for $1 < p <\infty$. This is made possible thanks to smooth orthogonal projection…

We study strongly measurable random bounded operators on separable Hilbert spaces and analyze two simple iterations driven by independent random positive contractions. The first, a Kaczmarz-like iteration, converges in mean square and…

In this paper we characterize $\sqrt{2}$-1-uniform $J$-Parseval fusion frames in a Krein space $\mathbb{K}$. We provide a few results regarding construction of new $J$-tight fusion frame from given $J$-tight fusion frames. We also…

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

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…

In this paper we introduce and show some new notions and results on cg-frames of Hilbert spaces. We define cg-orthonormal bases for a Hilbert space H and verify their properties and relations with cg-frames. Actually, we present that every…

Motivated by the dynamical sampling problem, we study frames in an infinite dimensional Hilbert space generated by the iterates of a bounded operator T, also known as dynamical frames. We first characterize the operators that generate…