Parabolic Martin Boundaries and Asymptotic Formulas of Heat Kernels for One-Dimensional Elliptic Operators with Periodic Coefficients |
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| Authors: | Minoru Murata Tetsuo Tsuchida |
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| Affiliation: | 1.Department of Mathematics,Tokyo Institute of Technology,Tokyo,Japan;2.Department of Mathematics,Meijo University,Nagoya,Japan |
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| Abstract: | We determine the Martin boundary of R × (???∞?, 0) for operators (partial_t+L), where L is a one-dimensional second-order elliptic operator with periodic coefficients. We also give long-time asymptotic formulas of heat kernels generated by L in the case that the ratio of the spatial variable to the time variable is large or small. |
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