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Hearing the shape of an annular drum

Published online by Cambridge University Press:  17 February 2009

H. P. W. Gottlieb
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 4 , April 1983 , pp. 435 - 438
Copyright
Copyright © Australian Mathematical Society 1983

References

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