Turkish Journal of Mathematics
Abstract
The Cauchy problem for the equation \begin{equation} Mw\equiv \sum_{j=0}^m\sum_{s=0}^{l_j}a_{s,j}\frac{\partial^{s+j}w(z_1,z_2)}{\partial z_1^s\partial z_2^j}=0 \end{equation} \begin{equation} \frac{\partial^nw(z_1,z_2)}{\partial z_2^n}\mid_{z_{2}=0}=\varphi_n(z_1), n=0,1,\ldots , m-1 \end{equation} is investigated under the condition $l_j\leq l_m, j=0,1,\ldots,m-1$. 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.
DOI
-
First Page
59
Last Page
66
Recommended Citation
KOROBEINIK, YU. F. (2000) "Representing Systems of Exponentials and Projection on Initial Data in the Cauchy Problem," Turkish Journal of Mathematics: Vol. 24: No. 1, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol24/iss1/4
