Uncertainty principles for the generalized Fourier transform associated to a Dunkl-type operator

2015 ◽  
Vol 95 (9) ◽  
pp. 1930-1956 ◽  
Author(s):  
Hatem Mejjaoli
Keyword(s):  
Fourier Transform ◽  
Type Operator ◽  
Uncertainty Principles ◽  
Generalized Fourier Transform

Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform

2016 ◽  
Vol 27 (03) ◽  
pp. 1650019 ◽  
Author(s):  
Troels Roussau Johansen
Keyword(s):  
Fourier Transform ◽  
Young Inequality ◽  
Uncertainty Principles ◽  
Weighted Inequalities ◽  
Generalized Fourier Transform ◽  
Pitt’S Inequality ◽  
Uncertainty Inequalities

We obtain several versions of the Hausdorff–Young and Hardy–Littlewood inequalities for the [Formula: see text]-generalized Fourier transform recently investigated at length by Ben Saïd, Kobayashi, and Ørsted. We also obtain a number of weighted inequalities — in particular Pitt’s inequality — that have application to uncertainty principles. Specifically we obtain several analogs of the Heisenberg–Pauli–Weyl principle for [Formula: see text]-functions, local Cowling–Price-type inequalities, Donoho–Stark-type inequalities and qualitative extensions. We finally use the Hausdorff–Young inequality as a means to obtain entropic uncertainty inequalities.

scholarly journals A generalized Fourier transform approach to risk measures

2010 ◽  
Vol 2010 (01) ◽  
pp. P01005 ◽  
Author(s):  
Giacomo Bormetti ◽  
Valentina Cazzola ◽  
Giacomo Livan ◽  
Guido Montagna ◽  
Oreste Nicrosini
Keyword(s):  
Fourier Transform ◽  
Risk Measures ◽  
Generalized Fourier Transform
Sign in / Sign up

Export Citation Format

Share Document