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Proceedings of the London Mathematical Society Advance Access published online on April 2, 2008

Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn014
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© 2008 London Mathematical Society

Long-time asymptotics of heat kernels for one-dimensional elliptic operators with periodic coefficients

Tetsuo Tsuchida

Department of Mathematics
Meijo University
Shiogamaguchi
Tenpaku-ku
Nagoya 468-8502
Japan

Received 11 June 2007. Revision received 24 January 2008.

We give long-time asymptotics of heat kernels generated by one-dimensional second-order elliptic operators with periodic coefficients. As a by-product Gaussian bounds are also derived.


2000 Mathematics Subject Classification 35B27, 35B40, 35J10.


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