AI Summary & Key Takeaways
AI InsightIt 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.
📌 3 Key Takeaways
Abstract
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.
Özet
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.