Abstract
Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
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Chen, M. E., Explicit hounds of the first eigenvalue, Science in China, Ser. A, 2000, 43(10): 1051.
Chen, M. F., Wang, F. Y., Estimation of spectral gap for elliptic operators, Trans. Amer. Math. Soc., 1997, 349(3): 1239–1267.
Chen, M. F., Wang, F. Y., General formula for lower bound of the first eigenvalue, Science in China, Ser. A, 1997, 40(4): 384–394.
Chen, M. F., Estimation of spectral gap for Markov chains, Acta Math. Sin. New Series, 1996, 12(4): 337–360.
Chen, M. F., Analytic proof of dual variational formula for the first eigenvalue in dimension one, Sci. in China, Ser. A, 1999, 42(8): 805–815.
Chen, M. F., Coupling, spectral gap and related topics (I), Chin. Sci. Bulletin, 1997, 42(16): 1321–1327.
Chen, M. F., Estimate of exponential convergence rate in total variation by spectral gap, Acta Math. Sin. Ser. A ( in Chinese), 1998, 41(1): 1–6.
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Chen, M. Variational formulas and approximation theorems for the first eigenvalue in dimension one. Sci. China Ser. A-Math. 44, 409–418 (2001). https://doi.org/10.1007/BF02881877
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DOI: https://doi.org/10.1007/BF02881877