Geodesic
Theorems of Wiman--Valiron type for solutions of parabolic equations
Sbornik. Mathematics, Tome 43 (1982) no. 1, pp. 63-84

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In this paper estimates of Wiman–Valiron type are established for solutions of evolution equations of the form \begin{equation} u'(t)+A(t)u(t)=0 \end{equation} in a Hilbert space, where $A(t)$ is a positive definite selfadjoint operator with discrete spectrum. In the case of a constant operator $A$ the results characterize the rate of growth of the function $\|u(t)\|$ as $t\to+0$ in terms of the rate of growth of the Fourier coefficients of the initial data. Bibliography: 18 titles. 
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     author = {N. M. Suleimanov},
     title = {Theorems of {Wiman--Valiron} type for solutions of parabolic equations},
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N. M. Suleimanov. Theorems of Wiman--Valiron type for solutions of parabolic equations. Sbornik. Mathematics, Tome 43 (1982) no. 1, pp. 63-84. http://geodesic.mathdoc.fr/item/SM_1982_43_1_a2/