A proof of the completeness of Lamb modes
- Jean-Luc Akian
Abstract
The aim of this paper is to give a precise proof of the completeness of
Lamb modes and associated modes. This proof is relatively simple and
short but relies on two powerful mathematical theorems. The first one is
a theorem on elliptic systems with a parameter due to Agranovich and
Vishik. The second one is a theorem due to Locker which gives a
criterion to show the completeness of the set of generalized
eigenvectors of a Hilbert-Schmidt discrete operator.26 Mar 2021Submitted to Mathematical Methods in the Applied Sciences 27 Mar 2021Submission Checks Completed
27 Mar 2021Assigned to Editor
06 Apr 2021Reviewer(s) Assigned
29 Jun 2021Review(s) Completed, Editorial Evaluation Pending
30 Jun 2021Editorial Decision: Revise Minor
05 Aug 20211st Revision Received
05 Aug 2021Submission Checks Completed
05 Aug 2021Assigned to Editor
10 Aug 2021Reviewer(s) Assigned
30 Aug 2021Review(s) Completed, Editorial Evaluation Pending
31 Aug 2021Editorial Decision: Accept
Feb 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 3 on pages 1402-1419. 10.1002/mma.7860 
