& psi;DOs with radial symbols and spaces of type G
FILOMAT(2023)
摘要
We investigate various G type spaces on Rd+ and their relations with the Gelfand-Shilov S type spaces on R2d through the mapping w : R2d-* Rd+, w(x, & xi;) = (2x21 + 2 & xi;21, ... , 2x2d + 2 & xi;2d). Sufficient conditions for the hypoellipticity of symbols originating from the coordinante radial symbols in G type spaces are also given. Two open problems explained in the introduction are posed.
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关键词
Pseudo-differential operators with radial symbols,Gelfand-Shilov regularity,Hermite expansions,Laguerre expansions
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