离散型p次Dirichlet型第一特征值
First Eigenvalue of p-Dirichlet Forms in Discrete Settings
设μ=(μi)i ≥ 0为Z+上的测度且p>1,考虑下述离散型p次 Dirichlet型Dp(f)=∑i=0∞μibi(fi-fi+1)(fip-1-fi+1p-1),f ≥ 0,其中 (bi)i ≥ 0 为Z+上的正序列.本文旨在给出空间 Lp(μ)上p次Dirichlet型Dp(f)所对应的第一特征值λ0,p=inf{Dp(f):‖f‖p=1,f非负且具有紧支撑}的上下界精细估计.
Let μ=(μi)i ≥ 0 be a measure on Z+:={0, 1, 2,...}, and p > 1. Consider the following p-Dirichlet form Dp(f)=∑i=0∞ μibi(fi-fi+1)(fip-1-fi+1p-1), f ≥ 0, where (bi)i ≥ 0 is a positive sequence. The purpose of this paper is to obtain upper and lower bounds for the first eigenvalue of p-Dirichlet form Dp(f) λ0,p=inf{Dp(f):‖f‖p=1, f ≥ 0 and has compact support}, where ‖f‖p=(∑i=0∞μifip)1/p.
特征值 / p次Dirichlet型 / 生灭过程 {{custom_keyword}} /
eigenvalue / p-Dirichlet form / birth-death processes {{custom_keyword}} /
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