Functions which are Fourier transforms of distributions
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 کاملOn Fourier Transforms of Radial Functions and Distributions
We find a formula that relates the Fourier transform of a radial function on R with the Fourier transform of the same function defined on R. This formula enables one to explicitly calculate the Fourier transform of any radial function f(r) in any dimension, provided one knows the Fourier transform of the one-dimensional function t 7→ f(|t|) and the two-dimensional function (x1, x2) 7→ f(|(x1, x...
متن کاملGeneralized Fourier Transforms of Distributions
In [1], R. A. Kunze has presented a notion of generalized Fourier transform of functions on locally compact abelian groups. The point of this paper is to extend this idea in the direction of distribution theory and to present some initial results on this generalized Fourier transform of distributions. In a later paper we hope to investigate in detail the domain, range, and kernel of this transf...
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 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...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1981
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-44-1-143-144