## 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)

### MSC:

 34G10 Linear differential equations in abstract spaces
Full Text:

### References:

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