& psi;DOs with radial symbols and spaces of type G

FILOMAT（2023）

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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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