On the Cauchy problem in Banach scales with compact embeddings. (English. Russian original) Zbl 0878.34054

Sib. Math. J. 37, No. 5, 1028-1036 (1996); translation from Sib. Mat. Zh. 37, No. 5, 1167-1175 (1996).
The main result is the following statement: Let \(B_\rho\) \((0<\rho<\infty)\) be a \(K\)-scale of Banach spaces and let \(L_1,\dots,L_j\) be a finite collection of singular operators satisfying \[ |Lu|_{\rho_1}\leq{\omega\over \rho_2-\rho_1} |u|_{\rho_2},\quad\omega= \text{const}>0. \] Then there is an equivalent \(K\)-scale \(B_\rho'\) such that \(L=L_i\) \((i=1,\dots,j)\) satisfy the quasidifferential estimate \[ |Lu|_{\rho}\leq {\partial\over\partial\rho} |u|_{\rho}. \]
Reviewer: R.Manthey (Jena)


34G10 Linear differential equations in abstract spaces
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