We investigate the properties of the Moyal multiplier algebras for the generalized Gelfand-Shilov spaces \(S_{{a_k}}^{{b_n}}\). We prove that these algebras contain Palamodov spaces of type \({\mathscr{E}}\), and establish continuity properties of the operators with Weyl symbols in this class. Analogous results are obtained for the projective version of the spaces of type S and are extended to the multiplier algebras for various translation-invariant star products.

中文翻译：

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S型广义空间的乘子代数的刻画。

我们研究了广义Gelfand-Shilov空间\（S _ {{{a_k}} ^ {{b_n}} \）的Moyal乘数代数的性质。我们证明这些代数包含类型为\（{{mathscr {E}} \）的Palamodov空间，并在此类中建立具有Weyl符号的算子的连续性。对于S型空间的射影版本，获得了相似的结果，并将其扩展到各种平移恒星乘积的乘数代数。