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• W3007176550 abstract "All the known counterexamples to Kac' famous question can one hear the shape of a drum, i.e., does isospectrality of two Laplacians on domains imply that the domains are congruent, consist of pairs of domains composed of copies of isometric building blocks arranged in different ways, such that the unitary operator intertwining the Laplacians acts as a sum of overlapping local isometries mapping the copies to each other. We prove and explore a complementary positive statement: if an operator intertwining two appropriate realisations of the Laplacian on a pair of domains preserves disjoint supports, then under additional assumptions on it generally far weaker than unitarity, the domains are congruent. We show this in particular for the Dirichlet, Neumann and Robin Laplacians on spaces of continuous functions and on $L^2$-spaces." @default.
• W3007176550 created "2020-03-06" @default.
• W3007176550 creator A5022183111 @default.
• W3007176550 creator A5062799255 @default.
• W3007176550 date "2020-02-21" @default.
• W3007176550 modified "2023-09-27" @default.
• W3007176550 title "Disjointness-preserving operators and isospectral Laplacians" @default.
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• W3007176550 hasPublicationYear "2020" @default.
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