In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

Abstract. A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms are characteristic functions of set...

In the context of a general lattice Γ in Rn and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families, all the MSF wavelets, all the multiwavelets associated with a Multiresolution Analysis (MRA) of multiplicity d ≥ 1, and all the scaling functions. Moreover, we give several examples: in particular, we construct a single, MRA and C∞(Rn) wavelet, which ...

The paper generalizes Lawton s criteria for scaling vectors by means of Kronecker products Necessary and su cient conditions for the stability orthonormality of scaling vectors are provided in terms of their two scale symbols The paper is based on the results of Shen x Introduction Usually the construction of multiwavelets is based on a multiresolution anal ysis MRA with higher multiplicity In ...

In the context of a general lattice ? in R n and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families, all the MSF wavelets, all the multiwavelets associated with a Multiresolution Analysis (MRA) of multiplicity d 1; and all the scaling functions. Moreover , we give several examples: in particular, we construct a single, MRA and C 1 (R n) wavelet, whi...

Parseval frames can be thought of as redundant or linearly dependent coordinate systems for Hilbert spaces, and have important applications in such areas as signal processing, data compression, and sampling theory. We extend the notion of a Parseval frame for a fixed Hilbert space to that of a moving Parseval frame for a vector bundle over a manifold. Many vector bundles do not have a moving ba...

We study singly-generated wavelet systems on R that are naturally associated with rank-one wavelet systems on the Heisenberg group N . We prove a necessary condition on the generator in order that any such system be a Parseval frame. Given a suitable subset I of the dual of N , we give an explicit construction for Parseval frame wavelets that are associated with I . We say that g ∈ L(I×R) is Ga...

in this paper we study the duality of bessel and g-bessel sequences in hilbertspaces. we show that a bessel sequence is an inner summand of a frame and the sum of anybessel sequence with bessel bound less than one with a parseval frame is a frame. next wedevelop this results to the g-frame situation.

This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination of the elements in the original frame. Several examples are considered, such as a Fourier frame on a spiral. The procedure can be applied to the construction...

Motivated by the idea of J-frame for a Krein space K , introduced by Giribet et al. (J. I. Giribet, A. Maestripieri, F. Martnez Peŕıa, P. G. Massey, On frames for Krein spaces, J. Math. Anal. Appl. (1), 393 (2012), 122–137.), we introduce the notion of ζ − J-tight frame for a Krein space K . In this paper we characterize J-orthonormal basis for K in terms of ζ−J-Parseval frame. We show that a K...