期刊
INVERSE PROBLEMS
卷 21, 期 4, 页码 1391-1395出版社
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/21/4/013
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Penrose-Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently Zelditch raised the question whether such billiards also have the same eigenvalue spectrum for the Dirichlet Laplacian (conjecturing 'no'). Here we show that generically (in the class of smooth domains) the two members of a mushroom pair have different spectra.
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