Bound on the counting function for the eigenvalues of an infinite multistratified acoustic strip

✍ Scribed by Olivier Poisson

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 181 KB
• Volume: 22
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(199906)22:9<773::aid-mma62>3.0.co;2-h

✦ Synopsis

Let N( ) be the counting function of the eigenvalues associated with the self-adjoint operator !( (x, z) )) in the domain "1;]0, h[, h'0, with Neuman or Dirichlet conditions at z"0, h. If "1 in the exterior of a bounded rectangular region O, that is, for "x" large, then N( ) is known to be sublinear: the proof consists in the spectral analysis of a quadratic form obtained from a Green formula for !( (x, z) )) on O. In our case, the medium is multistrati"ed: the function (x, z) satis"es (x, z)" (z) for "x" large. Since the direct use of the previous proof fails, we modify the quadratic form and obtain the estimate N( ))C .