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 renewed interest in the subject related to its role in wavelet theory. For a glance of the recent development and work on frames and related topics, see [3, 4, 5, 6, 9]. In this note, we will use the regular double infinite matrices (see [9, 10]) to obtain the frame conditions and wavelet coefficients.