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- W2793000411 abstract "We consider the zeta function $zeta_Omega$ for the Dirichlet-to-Neumann operator of a simply connected planar domain $Omega$ bounded by a smooth closed curve. We prove that, for a fixed real $s$ satisfying $|s|>1$ and fixed length $L(partial Omega)$ of the boundary curve, the zeta function $zeta_Omega(s)$ reaches its unique minimum when $Omega$ is a disk.This result is obtained by studying the difference $zeta_Omega(s)-2big({L(partial Omega)over 2pi}big)^szeta_R(s)$, where $zeta_R$ stands for the classical Riemann zeta function. The difference turns out to be non-negative for real $s$ satisfying $|s|>1$. We prove some growth properties of the difference as $srightarrowpminfty$. Two analogs of these results are also provided." @default.
- W2793000411 created "2018-03-29" @default.
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- W2793000411 date "2018-02-02" @default.
- W2793000411 modified "2023-10-04" @default.
- W2793000411 title "An inequality for the Steklov spectral zeta function of a planar domain" @default.
- W2793000411 doi "https://doi.org/10.4171/jst/196" @default.
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