离散型p次Dirichlet型第一特征值

林清春

数学学报 ›› 2018, Vol. 61 ›› Issue (6) : 951-962.

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PDF(435 KB)
数学学报 ›› 2018, Vol. 61 ›› Issue (6) : 951-962. DOI: 10.12386/A2018sxxb0086
论文

离散型p次Dirichlet型第一特征值

    林清春
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First Eigenvalue of p-Dirichlet Forms in Discrete Settings

    Qing Chun LIN
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摘要

μ=(μii ≥ 0为Z+上的测度且p>1,考虑下述离散型p次 Dirichlet型Dpf)=∑i=0μibifi-fi+1)(fip-1-fi+1p-1),f ≥ 0,其中 (bii ≥ 0 为Z+上的正序列.本文旨在给出空间 Lpμ)上p次Dirichlet型Dpf)所对应的第一特征值λ0,p=inf{Dpf):‖fp=1,f非负且具有紧支撑}的上下界精细估计.

Abstract

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):‖fp=1, f ≥ 0 and has compact support}, where ‖fp=(∑i=0μifip)1/p.

关键词

特征值 / p次Dirichlet型 / 生灭过程

Key words

eigenvalue / p-Dirichlet form / birth-death processes

引用本文

导出引用
林清春. 离散型p次Dirichlet型第一特征值. 数学学报, 2018, 61(6): 951-962 https://doi.org/10.12386/A2018sxxb0086
Qing Chun LIN. First Eigenvalue of p-Dirichlet Forms in Discrete Settings. Acta Mathematica Sinica, Chinese Series, 2018, 61(6): 951-962 https://doi.org/10.12386/A2018sxxb0086

参考文献

[1] Chen M. F., From Markov Chains to Non-equilibrium Particle Systems, World Scientific, Singapore, 2004.
[2] Chen M. F., Speed of stability for birth-death processes, Front. Math. China, 2010, 5(3):379-515.
[3] Chen M. F., Eigenvalues, Inequalities and Ergodic Theory, Springer, London, 2005.
[4] Chen M. F., Wang L., Zhang Y., Mixed eigenvalues of discrete p-Laplacian, Front. Math. China, 2014, 9(6):1261-1292.
[5] Chen M. F., Exponential convergence rate in entropy, Front. Math. China, 2007, 2(3):329-358.
[6] Farkas W., Jacob N., Schilling R. L. Feller semigroups, Lp sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols, Forum Math., 2001, 13:51-90.
[7] Mao Y. H., Zhang S. Y., Comparison of some Convergence Rates for Markov Processes, Acta Math. Sin., Chin. Ser., 2000, 43(6):1019-1027.
[8] Wang Z. K., Yang X. Q., Birth and Death Process and Markov Chains (in Chinese), Science Press, Beijing, 2005.
[9] Wang J. The First Eigenvalue of the Birth and Death Process of Lp Space (in Chinese), Submitted, 2014.
[10] Bobkov S. G., Tetali P., Modified logarithmic Sobolev inequalities in discrete settings, Journal of Theoretical Probability, 2006, 19(2):289-336.

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