Functions on the real line with nonnegative Fourier transforms
نویسندگان
چکیده
منابع مشابه
The Uncertainty Principle for Fourier Transforms on the Real Line
This paper will explore the heuristic principle that a function on the line and its Fourier transform cannot both be concentrated on small sets. We begin with the basic properties of the Fourier transform and show that a function and its Fourier transform cannot both have compact support. From there we prove the Fourier inversion theorem and use this to prove the classical uncertainty principle...
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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...
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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...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1994
ISSN: 0040-8735
DOI: 10.2748/tmj/1178225714