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Symmetrically global pseudo-differential operators are the generalization of pseudo-differential operators in which the symbol satisfies similar decay estimates due to differentiation with respect to x-variable and \( \xi \) -variable. These operators are also examples of operators on non-compact manifolds. With the help of the aforesaid operators, the compact embedding theorem for the Sobolev space, the Cauchy problem for SG-hyperbolic equations with constant multiplicities is discussed.

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Symmetrically Global Pseudo-Differential Operators Involving the Weinstein Transform

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  • 发表日期：

    2026年

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  • Santosh Kumar Upadhyay,
  • Mohd Sartaj

摘要

Symmetrically global pseudo-differential operators are the generalization of pseudo-differential operators in which the symbol satisfies similar decay estimates due to differentiation with respect to x-variable and \( \xi \) -variable. These operators are also examples of operators on non-compact manifolds. With the help of the aforesaid operators, the compact embedding theorem for the Sobolev space, the Cauchy problem for SG-hyperbolic equations with constant multiplicities is discussed.