[Un problème extrêmal pour transformée de Fourier de probabilité]
On résout un problème extrêmal concernant des fonctions caractéristiques soumises à la condition de s'annuler en un point fixé. L'origine du problème est l'étude de l'amplitude de survie d'un état quantique dans la dynamique de Schrödinger, et la solution exprime un phénomène curieux dans l'évolution des systèmes quantiques.
We study an extremal problem concerning the supremum of the Fourier transforms (characteristic functions) of probability distributions under the constraint that the Fourier transforms vanish at a fixed point. This problem arises from the investigation of the survival amplitudes of quantum states driven by Schrödinger dynamics, and has general and curious implications for the evolution pictures of quantum systems.
Accepté le :
Publié le :
Shunlong Luo 1 ; Zhengmin Zhang 2
@article{CRMATH_2005__341_5_293_0, author = {Shunlong Luo and Zhengmin Zhang}, title = {An extremal problem for {Fourier} transforms of probabilities}, journal = {Comptes Rendus. Math\'ematique}, pages = {293--296}, publisher = {Elsevier}, volume = {341}, number = {5}, year = {2005}, doi = {10.1016/j.crma.2005.07.021}, language = {en}, }
Shunlong Luo; Zhengmin Zhang. An extremal problem for Fourier transforms of probabilities. Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 293-296. doi : 10.1016/j.crma.2005.07.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.07.021/
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