Hearing the shape of an annular drum
- 1 January 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 24 (4) , 435-438
- https://doi.org/10.1017/s0334270000003799
Abstract
The asymptotic expansion for a spectral function of the Laplacian operator, involving geometrical properties of the domain, is demonstrated by direct calculation for the case of a doubly-connected region in the form of a narrow annular membrane. By utilizing a known formula for the zeros of the eigenvalue equation containing Bessel functions, the area, total perimeter and connectivity are all extracted explicitly.Keywords
This publication has 7 references indexed in Scilit:
- Harmonic properties of the annular membraneThe Journal of the Acoustical Society of America, 1979
- The ideal Bose-Einstein gas, revisitedPhysics Reports, 1977
- Distribution of eigenfrequencies for the wave equation in a finite domainAnnals of Physics, 1970
- Curvature and the eigenvalues of the LaplacianJournal of Differential Geometry, 1967
- On hearing the shape of a drumJournal of Combinatorial Theory, 1966
- Can One Hear the Shape of a Drum?The American Mathematical Monthly, 1966
- Can One Hear the Shape of a Drum?The American Mathematical Monthly, 1966