Fourier transforms of Dini-Lipschitz functions

The Fourier Transforms of Lipschitz Functions on the Heisenberg Group

We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the Heisenberg group Hn. We compare our conclusions with some previous results in the field.

Fourier Transforms of Lipschitz Functions on Certain Lie Groups

We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the special linear group of real matrices of order two. 2000 Mathematics Subject Classification. 42A38, 44A15, 42C99, 44A05.

Self Fourier functions and fractional Fourier transforms

It was shown [ 21 that any SFF can be decomposed in this manner. Thus, F(x) is an SFF if, and only if, it can be expressed as the sum of four functions in the form of the above equation. Additional SFF studies are reported in refs. [ 3-51. Another issue that has been recently investigated is the fractional Fourier transform [ 6-91. Two distinct definitions of the fractional Fourier transform ha...

Bounded Functions and Fourier Transforms

1. Statement of the principal result. The class of sequences obtainable as Fourier coefficients of measures on the circle group presents numerous structure problems of interest. Amongst the earliest results somewhat akin to that stated below appear Banach's theorems about lacunary coefficients; see e.g., [4, pp. 215-220]. More recently Helson [3] has studied analogous questions when the group c...

Surface Measures - Maximal Functions and Fourier Transforms