Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in L2
نویسندگان
چکیده
منابع مشابه
An Uncertainty Principle for the Dunkl Transform
The Dunkl transform is an integral transform on R" which generalises the classical Fourier transform. On suitable function spaces, it establishes a natural correspondence between the action of multiplication operators on one hand and so-called Dunkl operators on the other. These are differential-difference operators, generalising the usual partial derivatives, which are associated with a finite...
متن کاملAn uncertainty inequality for Fourier-Dunkl series
An uncertainty inequality for the Fourier–Dunkl series, introduced by the authors in [Ó. Ciaurri and J. L. Varona, A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform, Proc. Amer. Math. Soc. 135 (2007), 2939–2947], is proved. This result is an extension of the classical uncertainty inequality for the Fourier series.
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This paper is in the spirit of several works on best constants problems in Sobolev type inequalities. A general reference on this subject is the recent book of Hebey [9]. These questions have many interests. At first, they are at the origin of the resolution of famous geometrical problems as Yamabe problem. More generally, they show how geometry and analysis interact on Riemannian manifolds and...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2016
ISSN: 0021-9045
DOI: 10.1016/j.jat.2015.10.002