Banach Frames, Double Infinite Matrices and Wavelet Coefficients
نویسنده
چکیده
In this paper we study the action of a double infinite matrix A on f ∈ H ν (weighted Banach space, 1 ≤ p ≤ ∞) and on its wavelet coefficients. Also, we find the frame condition for A−transform of f ∈ H ν whose wavelet series expansion is known.
منابع مشابه
Infinite matrices, wavelet coefficients and frames
We study the action of A on f ∈ L 2 (R) and on its wavelet coefficients, where A = (a lmjk) lmjk is a double infinite matrix. We find the frame condition for A-transform of f ∈ L 2 (R) whose wavelet series expansion is known. 1. Introduction. The notation of frame goes back to Duffin and Schaeffer [7] in the early 1950s to deal with the problems in nonharmonic Fourier series. There has been ren...
متن کاملIntrinsic Localization of Frames
Several concepts for the localization of a frame are studied. The intrinsic localization of a frame is defined by the decay properties of its Gramian matrix. Our main result asserts that the canonical dual frame possesses the same intrinsic localization as the original frame. The proof relies heavily on Banach algebra techniques, in particular on recent spectral invariance properties for certai...
متن کاملStructure of Wavelet Covariance Matrices and Bayesian Wavelet Estimation of Autoregressive Moving Average Model with Long Memory Parameter’s
In the process of exploring and recognizing of statistical communities, the analysis of data obtained from these communities is considered essential. One of appropriate methods for data analysis is the structural study of the function fitting by these data. Wavelet transformation is one of the most powerful tool in analysis of these functions and structure of wavelet coefficients are very impor...
متن کاملBanach frames in coorbit spaces consisting of elements which are invariant under symmetry groups
This paper is concerned with the construction of atomic decompositions and Banach frames for subspaces of certain Banach spaces consisting of elements which are invariant under some symmetry group. These Banach spaces – called coorbit spaces – are related to an integrable group representation. The construction is established via a generalization of the well-established Feichtinger-Gröchenig the...
متن کاملWiener’s Lemma for Infinite Matrices
The classical Wiener’s lemma and its various generalizations are important and have numerous applications in numerical analysis, wavelet theory, frame theory, and sampling theory. There are many different equivalent formulations for the classical Wiener’s lemma, with an equivalent formulation suitable for our generalization involving commutative algebra of infinite matrices W := {(a(j − j))j,j′...
متن کامل