数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1603-1626.doi: 10.1007/s10473-020-0601-z

• 论文 •    下一篇

CONTINUITY PROPERTIES FOR BORN-JORDAN OPERATORS WITH SYMBOLS IN HÖRMANDER CLASSES AND MODULATION SPACES

Maurice de GOSSON1, Joachim TOFT2   

  1. 1. Faculty of Mathematics, NuHAG, University of Vienna, Vienna, Austria;
    2. Department of Mathematics, Linnæus University, Växjö, Sweden
  • 收稿日期:2019-09-06 修回日期:2020-05-13 出版日期:2020-12-25 发布日期:2020-12-30
  • 通讯作者: Joachim TOFT,E-mail:joachim.toft@lnu.se E-mail:joachim.toft@lnu.se
  • 作者简介:Maurice de GOSSON,E-mail:maurice.degosson@gmail.com
  • 基金资助:
    Maurice de Gosson has been supported by the Austrian research agency FWF (grant number P27773).

CONTINUITY PROPERTIES FOR BORN-JORDAN OPERATORS WITH SYMBOLS IN HÖRMANDER CLASSES AND MODULATION SPACES

Maurice de GOSSON1, Joachim TOFT2   

  1. 1. Faculty of Mathematics, NuHAG, University of Vienna, Vienna, Austria;
    2. Department of Mathematics, Linnæus University, Växjö, Sweden
  • Received:2019-09-06 Revised:2020-05-13 Online:2020-12-25 Published:2020-12-30
  • Contact: Joachim TOFT,E-mail:joachim.toft@lnu.se E-mail:joachim.toft@lnu.se
  • Supported by:
    Maurice de Gosson has been supported by the Austrian research agency FWF (grant number P27773).

摘要: We show that the Weyl symbol of a Born-Jordan operator is in the same class as the Born-Jordan symbol, when Hörmander symbols and certain types of modulation spaces are used as symbol classes. We use these properties to carry over continuity, nuclearity and Schatten-von Neumann properties to the Born-Jordan calculus.

关键词: quantization, Schatten-von Neumann, Feffermann-Phong's inequality

Abstract: We show that the Weyl symbol of a Born-Jordan operator is in the same class as the Born-Jordan symbol, when Hörmander symbols and certain types of modulation spaces are used as symbol classes. We use these properties to carry over continuity, nuclearity and Schatten-von Neumann properties to the Born-Jordan calculus.

Key words: quantization, Schatten-von Neumann, Feffermann-Phong's inequality

中图分类号: 

  • 35S99