The functions which operate on Fourier transforms
نویسندگان
چکیده
منابع مشابه
On Functions Which Are Fourier Transforms
1. Let G be a locally compact and abelian group, Gl the dual group. Through this paper, "Ml will denote the set of all bounded Radon measure n on G; this set will be considered as a Banach algebra when provided with the customary norm as the dual of the space Co(G) defined below and with the ring product defined as convolution. If /iGM1, its Fourier transform is by definition the bounded and co...
متن کاملSelf 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...
متن کاملOn Positive Functions with Positive Fourier Transforms
Using the basis of Hermite–Fourier functions (i.e. the quantum oscillator eigenstates) and the Sturm theorem, we derive constraints for a function and its Fourier transform to be both real and positive. We propose a constructive method based on the algebra of Hermite polynomials. Applications are extended to the 2-dimensional case (i.e. Fourier–Bessel transforms and the algebra of Laguerre poly...
متن کاملBounded 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...
متن کاملThe 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.
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1959
ISSN: 0001-5962
DOI: 10.1007/bf02559571