Uncertainty Principles for the Dunkl-Wigner Transforms
نویسندگان
چکیده
منابع مشابه
Uncertainty principles and optimally sparse wavelet transforms
In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that, we introduce a framework for analyzing localization aspects of window functions. Our localization theory diverges from the conventional theory in two ways. Fi...
متن کاملAn 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 کاملWigner functions and Weyl transforms for pedestrians
Wigner functions and Weyl transforms of operators offer a formulation of quantum mechanics that is equivalent to the standard approach given by the Schrödinger equation. We give a short introduction and emphasize features that give insight into the nature of quantum mechanics and its relation to classical physics. A careful discussion of the classical limit and its difficulties is also given. T...
متن کاملHermite Functions and Uncertainty Principles for the Fourier and the Windowed Fourier Transforms
We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on R which may be written as P (x) exp(Ax, x), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f̂(y). We also give the best constant in uncertainty principles of Gelf’and Shilov type. We then obtain sim...
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: Journal of Operators
سال: 2016
ISSN: 2314-5064,2314-5072
DOI: 10.1155/2016/7637346