A discrete Hardy’s uncertainty principle and discrete evolutions
- 18 Downloads
In this paper we give a discrete version of Hardy’s uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy’s principle. Moreover, we give an interpretation of this principle in terms of decaying solutions to the discrete Schrödinger and heat equations.
Unable to display preview. Download preview PDF.
- N. B. Andersen, A connection between the uncertainty principles on the real line and on the circle, arXiv:1307.4904v1 [math.FA].Google Scholar
- H. Dym and H. P. McKean Jr., Fourier Series and Integrals, Probability and Mathematical Statistics, Vol. 14, Academic Press, New York–London, 1972.Google Scholar
- T. N. T. Goodman, and S. S. Goh, Uncertainty principles and optimality on circles and spheres, in Advances in Constructive Approximation: Vanderbilt 2003, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2004, pp. 207–218.Google Scholar
- NIST Digital Library ofMathematical Functions. http://dlmf.nist.gov/, Release 1.0.10 of 2015-08-07.Google Scholar
- E. M. Stein and R. Shakarchi, Princeton Lecture in Analysis II. Complex Analysis, Princeton University Press, Princeton, NJ, 2003.Google Scholar