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Hypoellipticity for operators of infinitely degenerate Egorov type

Hypoellipticity for operators of infinitely degenerate Egorov type

We study the hypoellipticity for the operator (1) $P=D_{\iota}+i\alpha(t)b(t, x, D_{X})$ in $R_{t}\times R_{X}^{n}$ , where $i=\sqrt{-1}$ and $\alpha(t)$ is a $C^{\infty}$ function satisfying(2)Here $b(t, x, \xi)\in C^{\infty}(R_{t}, S_{1,0}^{1}(R_{X}^{n}))$ is a classical symbol for any fixed $t$ .We as- sume the principal symbol $b_{1}$ of $b$ is real valued.We denote …