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Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation |
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| Authors: | Sergio Albeverio Anne Boutet de Monvel-Berthier Zdzisław Brzeźniak |
| Affiliation: | (1) Fakultät für Mathematik, Ruhr Universität, 44780 Bochum, Germany: CERFIM;(2) BiBoS-Research Centre, Universität Bielefeld, 33615 Bielefeld, Germany;(3) Laboratoire de Physique Mathématique et géométrie EP 0004, Université Paris VII (Denis Diderot), 2 place Jussieu, 75251 Paris Cedex 05, France;(4) Present address: Department of Pure Mathematics, The University of Hull, HU6 7RX Hull, UK |
| Abstract: | We develop an approach by finite dimensional approximations for the study of infinite dimensional oscillatory integrals and the relative method of stationary phase. We provide detailed asymptotic expansions in the nondegenerate as well as in the degenerate case. We also give applications to the derivation of detailed asymptotic expansions in Planck's constant for the Schrödinger equation. |
| Keywords: | 58D30 35Q40 81Q20 46N50 58C27 58F05 35S30 35C20 81Q05 |
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