The wavelet transform on spaces of type S

Source abstract

The continuous wavelet transform is studied on certain Gel'fand–Shilov spaces of type S . It is shown that, for wavelets belonging to the one type of S -space defined on R, the wavelet transform is a continuous linear map of the other type of the S -space into a space of the same type (latter type) defined on R × R + . The wavelet transforms of certain ultradifferentiable functions are also investigated.