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- W212760886 abstract "The classical inverse problem of the determination of a smooth simply-connected planar domain by its Steklov spectrum [1] is equivalent to the problem of the reconstruction, up to conformal equivalence, a positive function $$a in C^infty (mathbb{S})$$ on the unit circle $$(mathbb{S}) = left{ {e^{itheta } } right}$$ from the spectrum of the operator aΛ e , where Λ e = (−d 2/dθ 2)1/2. We introduce 2k-forms Z k (a) (k = 1, 2,... ) of the Fourier coefficients of a, called the zeta-invariants. These invariants are determined by the eigenvalues of aΛ e . We study some properties of the forms Z k (a); in particular, their invariance under the conformal group. A few open questions about zeta-invariants is posed at the end of the article." @default.
- W212760886 created "2016-06-24" @default.
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- W212760886 date "2015-07-01" @default.
- W212760886 modified "2023-10-17" @default.
- W212760886 title "Zeta-invariants of the Steklov spectrum of a planar domain" @default.
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- W212760886 doi "https://doi.org/10.1134/s0037446615040114" @default.
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