TY  - JOUR
ID  - Turner2020
LB  - Turner2020
AU  - Turner, John Wm.
TI  - Echoes and glimpses of a distant drum
ST  - Echoes and glimpses of a distant drum
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 6
SP  - 737
EP  - 750
DO  - https://doi.org/10.7494/OpMath.2020.40.6.737
UR  - https://doi.org/10.7494/OpMath.2020.40.6.737
AB  - To what extent does the spectrum of the Laplacian operator on a domain \(D\) with prescribed boundary conditions determine its shape? This paper first retraces the history of this problem, then Kac's approach in terms of a diffusion process with absorbing boundary conditions. It is shown how the restriction to a polygonal boundary for \(D\) in this method, which required taking the limit of an infinite number of sides to obtain a smooth one, can be avoided by using the Duhamel method.
KW  - Kac drum problem
KW  - inverse methods
KW  - diffusion process
SN  - 1232-9274
ER  -