Analytic proof of dual variational formula for the first eigenvalue in dimension one

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 42, Issue 8, 1999, Pages 805-815

  Chen, Mufa ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Elliptic operator; Infinite matrix; Neumann and Dirichlet eigenvalue; The first eigenvalue variational formula

Indexed keywords

EID: 0042762343     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02884267     Document Type: Article

References (9)

1. Chen, M. F., From Markov Chains to Non-Equilibrium Particle Systems, Singapore: World Scientific, 1992.
2. Chen, M. F., Wang, F. Y., Estimation of spectral gap for elliptic operators, Trans. Amer. Math. Soc., 1997, 349: 1209.
3. Chen, M. F., Estimation of spectral gap for Markov chains, Acta Math. Sin., New Series, 1996, 12(4): 337.
4. Chen, M. F., Wang, F. Y., General formula for lower bound of the first eigenvalue on Riemannian manifolds, Science in China, Ser. A, 1994, 40(4): 384.
5. Chen, M. F., Wang, F. Y., Application of coupling method to the first eigenvalue on manifold, Science in China, Ser. A, 1993, 37(1): 1.
6. Chen, M. F., Estimate of exponential convergence rate in total variation by spectral gap, Acta Math. Sin., New Series 1998, 14(1): 9.
7. Chen, M. F., Wang, F. Y., Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap, Chin. Sci. Bull., 1998, 43(18): 1516.
8. Diaconis, P., Stroock, D. W., Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Prob., 1991, 1(1): 36.
9. Saloff-Coste, L., Lectures on finite Markov chains, in Lectures on Probability Theory and Statistics (ed. Bernard, D.), LNM 1665, Berlin: Springer-Verlag, 1997, 301.