Spectral structure of the Neumann–Poincaré operator on tori
作者： Kazunori Ando , Yong-Gwan Ji , Hyeonbae Kang , Daisuke Kawagoe , Yoshihisa Miyanishi
DOI: 10.1016/J.ANIHPC.2019.05.002
关键词: Hilbert space 、 Numerical range 、 Bounded function 、 Neumann–Poincaré operator 、 Mathematics 、 Operator (computer programming) 、 Eigenvalues and eigenvectors 、 Compact operator 、 Pure mathematics 、 Boundary (topology)
摘要: Abstract We address the question whether there is a three-dimensional bounded domain such that Neumann–Poincare operator defined on its boundary has infinitely many negative eigenvalues. It proved in this paper tori have property. done by decomposing into self-adjoint compact operators Hilbert space circle using toroidal coordinate system and Fourier basis, then proving numerical range of decomposition both positive values.
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