Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2020-11-22 , DOI: 10.1007/s00023-020-00979-1 Pavel Kurasov , Jacob Muller
The spectra of n-Laplacian operators \((-\Delta )^n\) on finite metric graphs are studied. An effective secular equation is derived and the spectral asymptotics are analysed, exploiting the fact that the secular function is close to a trigonometric polynomial. The notion of the quasispectrum is introduced, and its uniqueness is proved using the theory of almost periodic functions. To achieve this, new results concerning roots of functions close to almost periodic functions are proved. The results obtained on almost periodic functions are of general interest outside the theory of differential operators.
中文翻译:
度量图和几乎周期函数上的n -Laplacians:I
研究了n-拉普拉斯算子\((-\ Delta)^ n \)在有限度量图上的谱。利用世俗函数接近三角多项式的事实,得出了一个有效的世俗方程,并分析了光谱的渐近性。介绍了准频谱的概念,并使用几乎周期函数的理论证明了其唯一性。为了实现这一点,证明了有关函数根的近似于周期性函数的新结果。在微分算子的理论之外,关于几乎周期函数获得的结果是普遍感兴趣的。