SPECTRAL ASYMPTOTIC BEHAVIOR FOR A CLASS OF SCHR DINGER OPERATORS ON 1-DIMENSIONAL FRACTAL DOMAINS

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Counting function Schr dinger operator Minkowski dimension.
• 年，卷（期）: 2001,（2）
• 页码范围: 117-132
• 页数: 16页
• 分类号: O175.9.
• 语种: 英文

摘要

In this paper, we study the spectral asymptotic behavior for a class of Schr dinger operators on 1-dimensional fractal domains. We have obtained, if the potential function is locally constant, the exact second term of the spectral asymptotics. In general, we give a sharp estimate for the second term of the spectral asymptotics.