论文标题
伪差异操作员，Wigner Transform和Weyl Transform on offinepoincaré集团
Pseudo-Differential Operators, Wigner Transform, and Weyl Transform on the Affine Poincaré Group
论文作者
论文摘要
在本文中，我们研究了对载体庞加莱组$ \ mathcal {p} _ {aff} $的谐波分析，该{aff} $，它是一个非潜在的组，并获得具有算法的伪差异操作员。更准确地说，我们研究了伪分化运算符在$ \ Mathcal {p} _ {aff} $上的有界性能。我们还为操作员值符号提供了必要且充分的条件，以使相应的伪差异操作员在Hilbert-Schmidt运算符的类别中。因此，我们获得了Trace Class pseudo-differential Operators在PoincaréAffineGroup $ \ MATHCAL {P} _ {AFF} $上的表征，并为这些跟踪类操作员提供跟踪公式。最后，我们研究了Wigner Transform，Weyl变换与PoincaréAffineGroup $ \ Mathcal {P} _ {aff} $上的操作员有价值的符号相关。
In this paper, we study harmonic analysis on the affine Poincaré group $\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness properties of pseudo-differential operators on $\mathcal{P}_{aff}$. We also provide a necessary and sufficient condition on the operator-valued symbols such that the corresponding pseudo-differential operators are in the class of Hilbert--Schmidt operators. Consequently, we obtain a characterization of the trace class pseudo-differential operators on the Poincaré affine group $\mathcal{P}_{aff}$, and provide a trace formula for these trace class operators. Finally, we study the Wigner transform, and Weyl transform associated with the operator valued symbol on the Poincaré affine group $\mathcal{P}_{aff}$.
