An inequality for the zeta function of a planar domainReport as inadecuate

An inequality for the zeta function of a planar domain - Download this document for free, or read online. Document in PDF available to download.

1 LPP - Laboratoire Paul Painlevé 2 Sobolev Institute of Mathematics

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 non-negativeness and growth properties for $\zeta \Omegas-2\big{L\partial \Omega\over 2\pi}\big^s\zeta Rs\ s\leq-1$, where $L\partial \Omega$ is the length of the boundary curve and $\zeta R$ stands for the classical Riemann zeta function.Two analogs of these results are also provided.

Keywords : inverse spectral problem zeta function Dirichlet-to-Neumann operator Steklov spectrum

Author: Alexandre Jollivet - Vladimir Sharafutdinov -



Related documents