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An Inverse Spectral Result for the Neumann Operator on Planar Domains

✍ Scribed by J. Edward

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
339 KB
Volume
111
Category
Article
ISSN
0022-1236

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✦ Synopsis

The Neumann operator is an operator on the boundary of a smooth manifold which maps the boundary value of a harmonic function to its normal derivative. In this paper, the Neumann operator on the boundary of smooth, bounded, simply connected planar domains is studied. The asymptotics of the eigenvalues are computed. The regularised zeta function for the Neumann operator at (z=-2) is computed. Study of the zeta function is then used to show that the unit disk is characterised by the spectrum of its Neumann operator. (i) 1993 Academic Press. Inc

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