Long time asymptotic expansions of heat kernels for perturbed Hill operators

Article type: Research Article

Authors: Murata, Minoru | Tsuchida, Tetsuo

Affiliations: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan. E-mail: minoru3@math.titech.ac.jp | Department of Mathematics, Meijo University, Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan. E-mail: tsuchida@meijo-u.ac.jp

Abstract: We obtain, by exploiting Jost functions, asymptotic expansions of Green functions of perturbed Hill operators with respect to the spectral parameter around the minima of the continuous spectra. From the Green function expansions, we derive asymptotic expansions for large time of heat kernels for perturbed Hill operators.

Keywords: long time asymptotics, heat kernel, perturbed Hill operator, Jost function

DOI: 10.3233/ASY-2012-1091

Journal: Asymptotic Analysis, vol. 79, no. 1-2, pp. 161-187, 2012