Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE CONVERGENCE RATE FOR SCHRÖDINGER OPERATORS WITH COMPLEX TIME

  • Tie Li (School of Mathematics and Statistics Hainan Normal University and Faculty of Mathematics Baotou Teachers' College Inner Mongolia University of Science and Technology) ;
  • Yaoming Niu (Faculty of Mathematics and Computer Engineering Ordos Institute of Technology) ;
  • Ying Xue (Faculty of Mathematics Baotou Teachers' College Inner Mongolia University of Science and Technology)
  • Received : 2023.08.31
  • Accepted : 2024.02.23
  • Published : 2024.11.01
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Abstract

In this paper, in one spatial dimension, we study the convergence rate for Schrödinger operators with complex time Pta,𝛾, which is defined by $${P^t_{a,{\gamma}}}f(x)={S^{t+it^{\gamma}}_a}f(x)=\int_{\mathbb{R}}{e^{ix{\xi}}\,e^{ix{\mid}{\xi}{\mid}^a}\,e^{-t^{\gamma}{\mid}{\xi}{\mid}^a}}{\hat{f}}({\xi})d{\xi},$$ where 𝛾 > 0 and a > 0. The convergence rate for Schrödinger operators with complex time is different from that of classical Schrödinger operators in Cao-Fan-Wang (Illinois J. Math. 62: 365-380, 2018).

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Acknowledgement

The authors would like to express their deep gratitude to the referees for their very careful reading, important comments and valuable suggestions.

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