Turkish Journal of Mathematics
Article Title
Representing Systems of Exponentials and Projection on Initial Data in the Cauchy Problem
DOI

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 , m1 \end{equation} is investigated under the condition $l_j\leq l_m, j=0,1,\ldots,m1$. 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.
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