Generalized continuously translated framelet Available to Purchase

Framelet or wavelet frame is a frame generated by a single function by means of discretely dilating and translating. We introduce a Continuously Translated Framelet (CTF) which is a frame generated by a single function in a separable Hilbert space by continuous translations and discrete dilations. We found a method to generalize CTF as a family of frames that was resulted from decomposing the CTF generator.