Weighted integrability of multiplicative Fourier transforms
The paper extends some results concerning the classical Fourier transform to the multiplicative Fourier transform (MFT) . In particular, the authors give conditions which ensure that a contraction of an MFT is also an MFT, criteria for determining whether a sufficiently smooth function with nonnegative MFT belongs to \(H^\omega\) or \(h^\omega\) (where \(\omega\) is the modulus of continuity), theorems analogous to the Boas conjecture for the Fourier sine and cosine transform and a sufficient condition for the weighted integrability of the MFT of a generalized contraction of a function.
contractions of functions and multiplicative Fourier transform
scientific article; zbMATH DE number 5816195