Orthonormal Dilations of Non-tight Frames
نویسنده
چکیده
We establish dilation theorems for non-tight frames with additional structure, i.e., frames generated by unitary groups of operators and projective unitary representations. This generalizes previous dilation results for Parseval frames due to Han and Larson [6] and Gabardo and Han [5]. We also extend the dilation theorem for Parseval wavelets, due to Dutkay, Han, Picioroaga, and Sun [4], by identifying the optimal class of frame wavelets for which dilation into an orthonormal wavelet is possible.
منابع مشابه
G-Frames, g-orthonormal bases and g-Riesz bases
G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.
متن کاملPopular Wavelet Families and Filters and Their Use
Glossary 5 Introduction 6 Definition of Wavelets 7 Definition of Filters 8 Multi-Resolution Analysis 9 Wavelet Decomposition and Reconstruction 10 Refinable Functions 11 Compactly Supported Orthonormal Wavelets 12 Parameterization of Orthonormal Wavelets 13 Biorthogonal Wavelets 14 Prewavelets 15 Tight Wavelet Frames 16 Tight Wavelet Frames over Bounded Domain 17 q-Dilated Orthonormal Wavelets ...
متن کاملGroups and Wavelets
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and groups acting on R. We also show how this action can give rise to wavelets, and in particular, MSF wavelets)in L(R). Introduction The classical wavelet system co...
متن کاملCompactly Supported Tight Wavelet Frames and Orthonormal Wavelets of Exponential Decay with a General Dilation Matrix
Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d × d dilation matrix M , we demonstrate in a constructive way that we can construct compactly supported tight M -wavelet frames and orthonormal M -wavelet bases in L2(R) of exponential decay, which are derived from compactly supported M -refinable functions,...
متن کاملOrthonormal Dilations of Parseval Wavelets
We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...
متن کامل