Volume growth and bounds for the essential spectrum for Dirichlet forms
Volume growth and bounds for the essential spectrum for Dirichlet forms
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DOI：
10.1112/jlms/jdt029
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发表时间：
2012-05
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影响因子：
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通讯作者：
Sebastian Haeseler;M. Keller;Radoslaw K. Wojciechowski
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文献类型：
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作者：
Sebastian Haeseler;M. Keller;Radoslaw K. Wojciechowski
我们考虑由具有消失杀伤项的常规狄利克雷形式产生的算子。我们根据相对于内在指标的指数体积增长给出了（基本）谱的底部界限。作为特殊情况，我们讨论图上的运算符。当以自然图距离（不是内在度量）测量体积增长时，我们讨论（无界）图拉普拉斯谱底部的正性阈值和基本谱底部的有限性。该阈值显示为三次多项式增长。
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases, we discuss operators on graphs. When the volume growth is measured in the natural graph distance (which is not an intrinsic metric), we discuss the threshold for positivity of the bottom of the spectrum and finiteness of the bottom of the essential spectrum of the (unbounded) graph Laplacian. This threshold is shown to lie at cubic polynomial growth.