Prestin, J., E. Quak, H. Rauhut, and K. Selig, On the connection of uncertainty principles for functions on the circle and on the real line, J. Fourier Anal. Appl. 9 (2003), 387-409. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Uncertainty Principles and Asymptotic Behavior - Goh, Goodman (2004) (Correct)
....j sin tj , this reduces to an uncertainty principle established in [12] When = 0, i.e. w is constant, this is equivalent to the case of even f in the uncertainty principle ; w(t) e : 1.5) The inequality (1. 5) was earlier proved in [1] Despite further study in [4] 5] 7] 9] and [10], it was not noted that the lower bound 1 4 in (1.5) is approached by the simple sequence of trigonometric polynomials p k (t) 1 cos t) k = 1; 2; Indeed we show near the end of Section 2 that for any 0, k = 1; 2; 1 4 1 Instead, 9] considered approaching the ....
....function f in (1.13) will attain or approximate similarly the lower bound in the corresponding multivariate uncertainty principle. Finally we consider uncertainty principles for functions on the unit n sphere S in R , n = 2; 3; For n = 2, such an uncertainty principle was derived in [10], but the techniques of the proof do not extend to n 3. In [12] an uncertainty principle was given for the general case n 2, but only for a function f on S which is radial, i.e. for some unit vector u, f(x) depends only on x u, In this case, putting x u = cos t; f(x) g(t) 0 t ....
[Article contains additional citation context not shown here]
J. Prestin, E. Quak, H. Rauhut, and K. Selig, On the connection of uncertainty principles for functions on the circle and on the real line, preprint.
Uncertainty Principles and Optimality on Circles and Spheres - Goodman, Goh (2004) (Correct)
No context found.
Prestin, J., E. Quak, H. Rauhut, and K. Selig, On the connection of uncertainty principles for functions on the circle and on the real line, J. Fourier Anal. Appl. 9 (2003), 387-409.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC