scholarly journals Pointwise fourier inversion: A wave equation approach

1997 ◽  
Vol 3 (6) ◽  
pp. 647-703 ◽  
Author(s):  
Mark A. Pinsky ◽  
Michael E. Taylor
Keyword(s):  
Wave Equation ◽  
Equation Approach ◽  
Fourier Inversion

scholarly journals The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum inℝ2with Robin boundary conditions

2001 ◽  
Vol 25 (11) ◽  
pp. 717-726 ◽  
Author(s):  
E. M. E. Zayed ◽  
I. H. Abdel-Halim
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Inverse Eigenvalue Problem ◽  
Robin Boundary Conditions ◽  
Two Dimensional ◽  
Equation Approach ◽  
Multiply Connected ◽  
Inverse Eigenvalue ◽  
Negative Laplacian ◽  
Robin Boundary

The spectral functionμˆ(t)=∑j=1∞exp(−itμj1/2), where{μj}j=1∞are the eigenvalues of the two-dimensional negative Laplacian, is studied for small|t|for a variety of domains, where−∞<t<∞andi=−1. The dependencies ofμˆ(t)on the connectivity of a domain and the Robin boundary conditions are analyzed. Particular attention is given to an arbitrary multiply-connected drum inℝ2together with Robin boundary conditions on its boundaries.

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