HEISENBERG–PAULI–WEYL UNCERTAINTY INEQUALITY FOR THE DUNKL TRANSFORM ON ℝd
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.
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl Transform
Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.
متن کاملHeisenberg Uncertainty Inequality for Gabor Transform
We discuss the Heisenberg uncertainty inequality for groups of the form K Rn , K is a separable unimodular locally compact group of type I. This inequality is also proved for Gabor transform for several classes of groups of the form K Rn . Mathematics subject classification (2010): Primary 43A32; Secondary 43A30, 22D10, 22D30, 22E25.
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl transform
Using a generalized spherical mean operator, we obtain the generalizationof Titchmarsh's theorem for the Dunkl transform for functions satisfyingthe Lipschitz condition in L2(Rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2012
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972712000780