The Cauchy problem for the equation \begin{equation} Mw\equiv \sumj=0m\sums=0ljas,j\frac{\partials+jw(z1,z2)}{\partial z1s\partial z2j}=0 \end{equation} \begin{equation} \frac{\partialnw(z1,z2)}{\partial z2n}\midz2=0=jn(z1), n=0,1,\ldots , m-1 \end{equation} is investigated under the condition lj\leq lm, j=0,1,\ldots,m-1. It is shown that the operator of projection of solution of (1) on its initial data (2) in a definite situation has a linear continuous right inverse which can be determined effectively with the help of representing systems of exponentials in the space of initial data.

The Cauchy problem for the equation \begin{equation} Mw\equiv \sumj=0m\sums=0ljas,j\frac{\partials+jw(z1,z2)}{\partial z1s\partial z2j}=0 \end{equation} \begin{equation} \frac{\partialnw(z1,z2)}{\partial z2n}\midz2=0=jn(z1), n=0,1,\ldots , m-1 \end{equation} is investigated under the condition lj\leq lm, j=0,1,\ldots,m-1. It is shown that the operator of projection of solution of (1) on its initial data (2) in a definite situation has a linear continuous right inverse which can be determined effectively with the help of representing systems of exponentials in the space of initial data.