ABSTRACT
We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle https://www.w3.org/1998/Math/MathML"> S 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq4430.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and the real line R, following the general formalism of Coherent States (CS) associated to unitary square integrable representations of the group https://www.w3.org/1998/Math/MathML"> SL ( 2 , R ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq4431.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . We also provide explicit admissibility and continuous frame conditions for wavelets on https://www.w3.org/1998/Math/MathML"> S 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq4432.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
