The Fourier method in the Cauchy problem and absolutely representing systems of exponentials. II (Q5926563)

This paper is a continuation of Part I [Differ. Equations 35, No. 12, 1693-1701 (1999); translation from Differ. Uravn. 35, No. 12, 1669-1676 (1999; Zbl 0971.35016)]. In Section 3 he gave two equivalent conditions for the Cauchy problem to be reciprocally bounded and solvable in \({\mathcal{H}}\{0,0\}\) for an arbitrary initial function \(\varphi\in{\mathcal{H}}\{0\}\). Also, in Section 4 he showed that under certain conditions the projection operator \(\Pi\) has the linear continuous right inverse \(\Pi^{-1}_{Rl}\) with explicit formulas and that the Cauchy problem has a solution of the same form linearly and continuously depending on \(\varphi\).