This article is cited in 2 papers

Theorems of Wiman–Valiron type for solutions of parabolic equations

N. M. Suleimanov


Abstract: 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.

UDC: 517.95

MSC: Primary 35K22, 35B40; Secondary 30D15

Received: 21.04.1980

 English version: Mathematics of the USSR-Sbornik, 1982, 43:1, 63–84

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